00:00:00.949 all right so we move into this chapter 00:00:03.61900:00:03.629 on heat exchangers I think I budgeted 00:00:05.84000:00:05.850 three lectures for heat exchangers 00:00:07.90900:00:07.919 simply because it's so prevalent out 00:00:10.61000:00:10.620 there if you go through a class like 00:00:13.19000:00:13.200 heat transfer you should know something 00:00:14.81000:00:14.820 about heat exchangers we'll talk about 00:00:17.48000:00:17.490 types of heat exchangers won't cover 00:00:19.25000:00:19.260 them all just to introduce you to a few 00:00:20.96000:00:20.970 types talk about the overall heat 00:00:23.12000:00:23.130 transfer coefficient you and maybe if we 00:00:25.67000:00:25.680 get into the log mean temperature 00:00:26.90000:00:26.910 difference we'll get there today so a 00:00:30.20000:00:30.210 concentric tube is just what it sounds 00:00:32.47900:00:32.489 like you have a tube and you have fluid 00:00:35.69000:00:35.700 flowing inside the tube I'll color code 00:00:37.60000:00:37.610 the hot fluid is red and we have fluid 00:00:42.35000:00:42.360 hot coming in and hot going out of a 00:00:45.65000:00:45.660 heat exchanger but you have another 00:00:48.35000:00:48.360 tubes like that and it's concentric and 00:00:54.47000:00:54.480 so what we'll have here is we'll have 00:00:57.41000:00:57.420 some other fluid maybe I color it purple 00:00:59.99000:01:00.000 come in this area flow in the annulus 00:01:05.02000:01:05.030 between the two tubes it then come out 00:01:08.45000:01:08.460 on this end so as I've shown the flow 00:01:12.64900:01:12.659 inside of the tube is moving from left 00:01:16.19000:01:16.200 to right and the float in the annulus is 00:01:19.76000:01:19.770 moving right to left and you would call 00:01:23.66000:01:23.670 that a counter flow concentric tube or 00:01:27.32000:01:27.330 double paul double pipe heat exchanger 00:01:31.39000:01:31.400 cross flow is a little harder to sketch 00:01:34.01000:01:34.020 but it's a number of illustrations in 00:01:36.26000:01:36.270 the textbook you could have round tubes 00:01:38.69000:01:38.700 and I'll have a bundle of them and flow 00:01:44.30000:01:44.310 inside each of those tubes 00:01:47.85900:01:47.869 maybe we show the hot fluid in the tubes 00:01:50.92900:01:50.939 coming out coming out coming out coming 00:01:53.24000:01:53.250 out coming out hard to show it all but 00:01:56.56900:01:56.579 then we have maybe cooler fluid flowing 00:01:58.78900:01:58.799 across the tubes just like you might 00:02:00.95000:02:00.960 think cross flow heat exchanger 00:02:04.30000:02:04.310 sometimes well almost all the time the 00:02:09.32000:02:09.330 two 00:02:10.08000:02:10.090 has some surface conditioning on the 00:02:13.17000:02:13.180 inside as well as on the outside to help 00:02:16.58900:02:16.599 promote heat transfer in real heat 00:02:19.41000:02:19.420 exchangers the other thing that can 00:02:22.65000:02:22.660 happen is they could introduce a finned 00:02:25.68000:02:25.690 material maybe you have circular fins 00:02:28.71000:02:28.720 around each of the tubes to help promote 00:02:33.00000:02:33.010 heat transfer or you could have a plate 00:02:35.60000:02:35.610 that connects a lot of them together and 00:02:39.53900:02:39.549 there's different configurations for 00:02:41.33900:02:41.349 that all right so one surface Tanner is 00:02:45.72000:02:45.730 often defend it's the air side that's 00:02:48.12000:02:48.130 been not the water side or the 00:02:50.19000:02:50.200 refrigerant side or the liquid side 00:02:53.56900:02:53.579 another is a shell and tube heat 00:02:55.74000:02:55.750 exchangers so what's the shell just as 00:02:58.89000:02:58.900 it might be a big shell and then you 00:03:01.86000:03:01.870 have a bunch of tubes a bundle of tubes 00:03:05.33900:03:05.349 that were on that are straight I'm going 00:03:08.36900:03:08.379 to show it them being straight it's easy 00:03:10.25900:03:10.269 to make a bunch of tubes that are 00:03:12.27000:03:12.280 straight and the flow then would go one 00:03:14.81900:03:14.829 way down through maybe 50 tubes or 100 00:03:19.08000:03:19.090 tubes going in that direction how do 00:03:22.17000:03:22.180 they get into the tube well you have a 00:03:24.36000:03:24.370 basically a manifold here where you have 00:03:27.69000:03:27.700 fluid coming in and the fluid coming in 00:03:32.67000:03:32.680 would then distribute and go inside each 00:03:36.03000:03:36.040 of the tubes well down at the end you 00:03:39.03000:03:39.040 have another plate and they exit out of 00:03:43.86000:03:43.870 the tubes they mix and because of the 00:03:47.94000:03:47.950 end cap they might flow back through 00:03:50.84900:03:50.859 another set of tubes a bunch of tubes 00:03:57.44900:03:57.459 that way maybe another 50 maybe 75 maybe 00:04:00.56900:04:00.579 a hundred tubes you could have big large 00:04:02.28000:04:02.290 heat exchangers doing this and then they 00:04:04.71000:04:04.720 pop out and they're collect and would 00:04:09.27000:04:09.280 discharge here that Inlet plenum and the 00:04:12.44900:04:12.459 outlet plenum are at the same end which 00:04:15.78000:04:15.790 is convenient for servicing or hooking 00:04:18.59900:04:18.609 it up and sir or you could have it on 00:04:20.67000:04:20.680 either end sometimes they'll have 00:04:24.06000:04:24.070 the tube bundle is a tube and it comes 00:04:27.00000:04:27.010 down and they're all u-shaped so they 00:04:30.33000:04:30.340 have a bend in that back think well 00:04:31.92000:04:31.930 that's a little harder to manufacture 00:04:33.54000:04:33.550 but they do have them like that as well 00:04:36.41000:04:36.420 what about the shell side well you would 00:04:39.66000:04:39.670 like the fluid to come in the shell side 00:04:41.82000:04:41.830 maybe over here and exit over here and 00:04:46.02000:04:46.030 you'd like to promote the heat transfer 00:04:47.79000:04:47.800 between the fluids so maybe you'd like 00:04:49.17000:04:49.180 the fluid on the shell side to go across 00:04:51.24000:04:51.250 the two bundles then across the tube 00:04:54.18000:04:54.190 bundles across the tube bundles across 00:04:57.57000:04:57.580 the two bundles and back out how would 00:05:00.06000:05:00.070 you do that well you would introduce 00:05:01.35000:05:01.360 baffles Baca jizz that would then force 00:05:06.45000:05:06.460 the flow across the tubes and I just 00:05:10.08000:05:10.090 sketch a few baffles in there so there's 00:05:13.65000:05:13.660 a lot of shell and tube heat exchangers 00:05:16.05000:05:16.060 different configurations lot of cross 00:05:19.80000:05:19.810 flow heat exchangers different 00:05:21.42000:05:21.430 configurations what we end up doing is 00:05:23.79000:05:23.800 we end up analyzing concentric tube heat 00:05:26.91000:05:26.920 exchangers because we can develop the 00:05:28.71000:05:28.720 mathematical framework and then we 00:05:30.84000:05:30.850 extrapolate that framework to the more 00:05:33.63000:05:33.640 complex which then rely on empirical 00:05:37.53000:05:37.540 data measurements from built heat 00:05:40.14000:05:40.150 exchangers that are tested in the lab 00:05:43.34000:05:43.350 one of the key parameters are going to 00:05:45.66000:05:45.670 be an overall heat transfer coefficient 00:05:47.25000:05:47.260 you well we're trying to move heat from 00:05:51.09000:05:51.100 one fluid through a material let's say 00:05:56.25000:05:56.260 that's a barrier that's a wall if you're 00:05:59.16000:05:59.170 thinking about tubes then then it's just 00:06:01.50000:06:01.510 through the tube wall and to another 00:06:04.98000:06:04.990 fluid or maybe from hot to cold it 00:06:07.83000:06:07.840 really doesn't matter I should have 00:06:09.90000:06:09.910 maybe put hot over on the left but 00:06:12.39000:06:12.400 anyway you have a fluid temperature T 00:06:14.64000:06:14.650 fluid you have a wall temperature let's 00:06:18.48000:06:18.490 say on the inside you have a wall 00:06:20.76000:06:20.770 temperature on the outside and then a 00:06:23.58000:06:23.590 fluid temperature on the outside so 00:06:25.92000:06:25.930 inside fluid temperature outside fluid 00:06:27.99000:06:28.000 temperature what do we have we have 00:06:29.67000:06:29.680 convective resistance one over H a on 00:06:33.42000:06:33.430 the inside we have some sort of wall 00:06:36.39000:06:36.400 resistance 00:06:37.67900:06:37.689 our W if it was unfinished a tube may be 00:06:42.65900:06:42.669 the natural log of the outer over D 00:06:45.41900:06:45.429 inner / 2 pi K L would be a good model 00:06:50.06900:06:50.079 for that resistance and then convective 00:06:53.30900:06:53.319 resistance on the outside 1 over H 00:06:55.97900:06:55.989 outside area outside that would be the 00:06:58.43900:06:58.449 most simple three resistors in series 00:07:02.08900:07:02.099 and if you sum them up you would get the 00:07:05.63900:07:05.649 total resistance so you could replace it 00:07:07.52900:07:07.539 by one resistor one equivalent resistor 00:07:10.85900:07:10.869 true and what you do is you say that 00:07:15.80900:07:15.819 equivalent resistance R equivalent would 00:07:18.17900:07:18.189 be the sum of those three resistors and 00:07:20.27900:07:20.289 we often describe it by an overall heat 00:07:24.54000:07:24.550 transfer coefficient u 1 over UA is an 00:07:29.66900:07:29.679 overall resistance the equivalent 00:07:32.96900:07:32.979 overall resistance from fluid to fluid 00:07:35.62900:07:35.639 so 1 over u a what is u then the overall 00:07:39.89900:07:39.909 heat transfer coefficient does it have 00:07:43.10900:07:43.119 the same thermal what are the SI units 00:07:47.24900:07:47.259 for the overall heat transfer 00:07:48.32900:07:48.339 coefficient they're the same as the H 00:07:51.82900:07:51.839 same as the H so it has watts per meter 00:07:54.92900:07:54.939 squared degrees C or Kelvin a lot of 00:07:59.57900:07:59.589 times what I'll do is how compute this 00:08:02.42900:08:02.439 are equivalent and I know that our 00:08:05.12900:08:05.139 equivalent is made up of an outside 00:08:07.76900:08:07.779 through the conduction through the wall 00:08:10.31900:08:10.329 and an inside and then I'll go back and 00:08:13.10900:08:13.119 I'll determine what percent each of 00:08:15.50900:08:15.519 these contributed to the resistance to 00:08:21.14900:08:21.159 heat transfer and which one you think is 00:08:23.63900:08:23.649 often negligible which offers a 00:08:26.63900:08:26.649 negligible thermal resistance to the 00:08:29.10000:08:29.110 heat transfer of the three components 00:08:33.11000:08:33.120 it's through the wall often it's made of 00:08:35.81900:08:35.829 aluminum or made of copper and often 00:08:42.32900:08:42.339 they're thin walled materials so it's 00:08:45.05900:08:45.069 it's a easy to get that what happens if 00:08:48.84000:08:48.850 I have some thinning going on on this 00:08:51.69000:08:51.700 side well what you can do is you can 00:08:56.61000:08:56.620 have the same H on the inside right here 00:09:00.06000:09:00.070 you would modify this term if it was 00:09:01.86000:09:01.870 finned you'd have one over the 00:09:03.90000:09:03.910 convection coefficient often thinning 00:09:06.15000:09:06.160 doesn't change the convection 00:09:07.74000:09:07.750 coefficient it just increases the area 00:09:10.56000:09:10.570 doesn't and so this area wouldn't just 00:09:14.04000:09:14.050 be the area on the inside but it'd be 00:09:15.81000:09:15.820 the thinned area on the inside but we 00:09:19.44000:09:19.450 know from the fins that you can have a 00:09:22.26000:09:22.270 lower temperature at the tip then at the 00:09:24.57000:09:24.580 base and so there's a fin parameter what 00:09:29.94000:09:29.950 is that fin parameter so this is how you 00:09:34.38000:09:34.390 would modify it if you had thinning on 00:09:36.57000:09:36.580 one side what is this eight or not 00:09:40.22000:09:40.230 overall that's right overall fin 00:09:42.84000:09:42.850 efficiency for that surface and you just 00:09:45.90000:09:45.910 have to go back and review that out of 00:09:47.76000:09:47.770 chapter three when we talked about fins 00:09:50.22000:09:50.230 and this is the total area of that 00:09:54.66000:09:54.670 thinned surface you'd say that accounts 00:09:57.78000:09:57.790 for the unexposed exposed base as well 00:10:00.84000:10:00.850 as the fins sticking out that's exactly 00:10:03.87000:10:03.880 right okay sometimes in real 00:10:10.47000:10:10.480 applications you have fouling here's one 00:10:12.78000:10:12.790 slide in one class for the whole topic 00:10:16.32000:10:16.330 of fouling and fouling is a big issue in 00:10:19.47000:10:19.480 practice that's just way it is I just 00:10:21.96000:10:21.970 don't have a lot of time to explore this 00:10:24.09000:10:24.100 as a topic but it's important because 00:10:26.42000:10:26.430 when you have hot oils or gases and you 00:10:30.63000:10:30.640 have deposits some corrosion some you 00:10:34.35000:10:34.360 know chemical reactions happening you 00:10:36.93000:10:36.940 can then get buildup of stuff which 00:10:39.57000:10:39.580 would not promote heat transfer but 00:10:41.61000:10:41.620 would add a resistance to heat transfer 00:10:43.40000:10:43.410 so we have a fouling factor what you do 00:10:46.62000:10:46.630 is you come in and you have one over you 00:10:49.80000:10:49.810 is basically one over H a for the 00:10:53.16000:10:53.170 convection but then you'd have are 00:10:55.31000:10:55.320 fouling you're adding a resistance to 00:10:59.22000:10:59.230 fouling plus then the resistance due to 00:11:01.71000:11:01.720 the wall etc so how do they modify it 00:11:04.98000:11:04.990 well 00:11:05.48000:11:05.490 for a bunch of different fluids and 00:11:07.69900:11:07.709 different service conditions and these 00:11:09.94900:11:09.959 change over a number of while it's in 00:11:12.86000:11:12.870 service sometimes they monitor the 00:11:15.05000:11:15.060 resistance they can detect how the the 00:11:17.21000:11:17.220 heat exchange is performing and then 00:11:18.98000:11:18.990 they'll take it out of service and clean 00:11:21.29000:11:21.300 it physically go in there and remove the 00:11:24.01900:11:24.029 scale and remove the deposits to reduce 00:11:27.62000:11:27.630 the fouling factor get it back to zero 00:11:29.93000:11:29.940 all right well you can see this is how 00:11:33.88900:11:33.899 the textbook reports a fouling factor 00:11:36.85000:11:36.860 what is that is that our double Prime 00:11:40.75000:11:40.760 yeah this is one of those be very 00:11:43.94000:11:43.950 careful right here if I was the author 00:11:46.63900:11:46.649 of the textbook or the editor the 00:11:48.56000:11:48.570 textbook I would tell them change your 00:11:50.78000:11:50.790 notation because this isn't a minority 00:11:53.51000:11:53.520 if you take a look at a lot of 00:11:55.13000:11:55.140 engineering literature is there a double 00:11:57.26000:11:57.270 Prime on this fouling factor know when 00:12:00.94900:12:00.959 you have Q and then you have Q Prime 00:12:03.53000:12:03.540 what was the prime on the Q often 00:12:05.90000:12:05.910 representing Q per unit length true and 00:12:10.55000:12:10.560 if you had Q double prime what that 00:12:12.74000:12:12.750 double prime represent Q per unit area 00:12:14.93000:12:14.940 and sometimes Q triple prime is Q per 00:12:18.23000:12:18.240 unit volume I know that sometimes you 00:12:21.01900:12:21.029 use prime for derivative time derivative 00:12:22.57900:12:22.589 you know second time derivative but 00:12:24.41000:12:24.420 that's not that's in more in mathematics 00:12:27.29000:12:27.300 classes but this is common notation to 00:12:30.44000:12:30.450 put prime double prime and triple prime 00:12:32.96000:12:32.970 per unit length per unit area per unit 00:12:34.67000:12:34.680 volume so but if you take a look at this 00:12:36.76900:12:36.779 this is not what it's saying it's not 00:12:38.96000:12:38.970 per unit area this is the correct units 00:12:42.13900:12:42.149 of the fouling factor it's the same as 00:12:44.99000:12:45.000 what you would find in a lot of other 00:12:46.37000:12:46.380 places its meter squared Kelvin per watt 00:12:50.07900:12:50.089 so if I want to add this resistance one 00:12:53.42000:12:53.430 over H a with the wall resistance with 00:12:55.79000:12:55.800 some fouling where do I put the a do I 00:12:59.99000:13:00.000 put the a here put the a there or do I 00:13:03.35000:13:03.360 have the R in the right place do I need 00:13:05.12000:13:05.130 to put it one over R we don't see what 00:13:08.09000:13:08.100 I'm saying I have a choice here I need 00:13:10.40000:13:10.410 that resistance a thermal resistance the 00:13:13.22000:13:13.230 correct formula is our faul divided by a 00:13:17.00000:13:17.010 and 00:13:18.63900:13:18.649 if you just take a look you SI units on 00:13:21.16000:13:21.170 that would be meters squared Kelvin per 00:13:24.60900:13:24.619 watt divided by meter squared cancels 00:13:27.24900:13:27.259 you get how much temperature difference 00:13:30.22000:13:30.230 per watt of heat transfer 00:13:33.30900:13:33.319 so that's are the good units for these 00:13:35.61900:13:35.629 for thermal resistances isn't it 00:13:37.67900:13:37.689 Kelvin per watt so right there just be 00:13:42.34000:13:42.350 very careful I found this notation a 00:13:44.67900:13:44.689 little I don't know clumsy for me 00:13:48.99900:13:49.009 conceptually it's it's I wish they would 00:13:51.24900:13:51.259 just have left that off and put an F 00:13:54.63900:13:54.649 there just call it the fouling factor 00:13:56.91900:13:56.929 and it's a thermal resistance and when 00:13:59.61900:13:59.629 you want to use it you need divide by 00:14:01.38900:14:01.399 the appropriate area all right if it's a 00:14:05.55900:14:05.569 thin surface it has a lot of area 00:14:07.66000:14:07.670 because of the thinning you have to 00:14:09.24900:14:09.259 divide by that appropriate area for all 00:14:11.59000:14:11.600 that thin surface okay so I already 00:14:15.69900:14:15.709 talked about how to modify one over you 00:14:18.00900:14:18.019 a with the adding fouling right so I 00:14:21.24900:14:21.259 already done that now let's talk about 00:14:24.69900:14:24.709 the temperature distribution so let's 00:14:27.04000:14:27.050 have a soft introduction to how the heat 00:14:30.30900:14:30.319 is transferred not jump into the math 00:14:32.19900:14:32.209 and get lost in the math quite right 00:14:34.11900:14:34.129 away so if we have a concentric tube 00:14:36.61000:14:36.620 heat exchanger and it's parallel flow 00:14:39.10000:14:39.110 what does that mean I'm gonna just kind 00:14:40.86900:14:40.879 of sketch it like this I know that's a 00:14:42.42900:14:42.439 very simple illustration and we'll put 00:14:44.73900:14:44.749 the hot fluid flowing from left to right 00:14:48.57900:14:48.589 going down there 00:14:49.66000:14:49.670 and I know that the annulus but I'm 00:14:52.36000:14:52.370 gonna show the fluid the cold fluid just 00:14:54.36900:14:54.379 be below this box and it's a parallel 00:14:57.46000:14:57.470 flow the cold fluid is flowing in the 00:15:00.28000:15:00.290 same direction in the annulus as the 00:15:04.21000:15:04.220 fluid that's in the inner pipe or the 00:15:06.81900:15:06.829 inner tube so we talked about the 00:15:09.69900:15:09.709 temperature hot coming in and the 00:15:12.06900:15:12.079 temperature hot going out which of those 00:15:15.00900:15:15.019 two hot temperatures is the lower value 00:15:18.60000:15:18.610 the out is a lower temperature go back 00:15:22.56900:15:22.579 to the basics and work conceptually 00:15:25.09000:15:25.100 through these problems how about this 00:15:27.30900:15:27.319 one the temperature cold in and the 00:15:30.57900:15:30.589 temperature cold out 00:15:32.53000:15:32.540 which of those two colds is the lower 00:15:35.83000:15:35.840 temperature the cold in is the lower 00:15:39.58000:15:39.590 temperature isn't it so when we plot 00:15:42.99000:15:43.000 temperature as a function of location X 00:15:47.41000:15:47.420 we're going to go from zero to the 00:15:50.20000:15:50.210 length of the heat exchanger if it was 00:15:52.54000:15:52.550 longer it would be more area promote 00:15:55.66000:15:55.670 more heat transfer and we'll plot the th 00:15:59.02000:15:59.030 in pot in right there and we'll start 00:16:02.65000:16:02.660 with the temperature cold in right there 00:16:05.37000:16:05.380 what do you think the profile looks like 00:16:08.05000:16:08.060 there could be a number of different 00:16:10.06000:16:10.070 configurations it'll be kind of a 00:16:13.63000:16:13.640 exponential that shape and maybe this 00:16:16.87000:16:16.880 shape so this would be the temperature 00:16:20.74000:16:20.750 of the hot out and the temperature of 00:16:22.84000:16:22.850 the cold out somebody says the hot 00:16:26.43000:16:26.440 hasn't gotten quite to the temperature 00:16:28.96000:16:28.970 of the cold out has it let's make this a 00:16:32.41000:16:32.420 very very long heat exchanger there it 00:16:36.01000:16:36.020 is now L is way out there could you ever 00:16:39.07000:16:39.080 have the hot coming out lower than the 00:16:42.58000:16:42.590 cold coming out temperature hot out 00:16:48.85000:16:48.860 could be lower not in a parallel flow 00:16:54.43000:16:54.440 heat exchanger if you went counter flow 00:16:59.88000:16:59.890 you would counter flows more common but 00:17:04.21000:17:04.220 that's a parallel flow that we just 00:17:05.65000:17:05.660 start with all right 00:17:07.09000:17:07.100 so we're gonna work with focusing on a 00:17:11.19900:17:11.209 little DX and what happens in the little 00:17:15.40000:17:15.410 section DX of this heat exchanger you 00:17:18.76000:17:18.770 could have a little DQ through and the 00:17:23.86000:17:23.870 little DQ could be represented by the 00:17:26.56000:17:26.570 local convection coefficient there times 00:17:29.56000:17:29.570 that small da that small area times the 00:17:33.67000:17:33.680 how hot it is at that location and how 00:17:36.82000:17:36.830 cold the fluid is at that location this 00:17:40.99000:17:41.000 da is often replaced by a P 00:17:44.54900:17:44.559 DX what does the P represent perimeter 00:17:47.94000:17:47.950 that's exactly right 00:17:49.11000:17:49.120 the perimeter and if I focused on the 00:17:53.31000:17:53.320 hot fluid what would happen is look is 00:17:57.81000:17:57.820 the direction of positive changing X 00:18:00.60000:18:00.610 going from 0 to L it's always in the 00:18:03.69000:18:03.700 traditional you know left to right isn't 00:18:07.20000:18:07.210 it ok so it would be mass flow rate of 00:18:12.26900:18:12.279 the hot fluid specific heat oops that's 00:18:15.50900:18:15.519 a C sub P sisa P of the hot fluid times 00:18:19.35000:18:19.360 the temperature change of the hot fluid 00:18:21.11900:18:21.129 the change in the temperature of the hot 00:18:23.36900:18:23.379 fluid with respect to x times DX well I 00:18:27.02900:18:27.039 have to put a negative sign there 00:18:29.90900:18:29.919 because what is the slope of that line 00:18:33.60000:18:33.610 right there it's negative and I'm always 00:18:38.15900:18:38.169 talking about moving a positive DX in 00:18:40.91900:18:40.929 the positive x direction all right when 00:18:45.01900:18:45.029 so this is the DQ that comes out of the 00:18:49.25900:18:49.269 hot we also talked about a positive DQ 00:18:54.23900:18:54.249 that goes into the cold would that be 00:18:57.26900:18:57.279 the mass flow rate of the cold specific 00:18:59.39900:18:59.409 heat of the cold and now the change the 00:19:02.43000:19:02.440 question is is we're talking about the 00:19:05.07000:19:05.080 same DQ these are all positive these are 00:19:08.60900:19:08.619 all positive right don't write one 00:19:11.12900:19:11.139 equation and say oh in that equation DQ 00:19:13.20000:19:13.210 is negative and now in this equation D Q 00:19:15.23900:19:15.249 is positive you could do it it'd be very 00:19:17.19000:19:17.200 confusing don't do it everything on the 00:19:20.22000:19:20.230 left-hand side of all of these three 00:19:22.01900:19:22.029 equations they're equal signs are 00:19:24.02900:19:24.039 positive all right so now what does what 00:19:29.66900:19:29.679 about the change in the temperature of 00:19:31.32000:19:31.330 the cold fluid with respect to X DX it's 00:19:35.90900:19:35.919 already positive by itself so I just do 00:19:39.72000:19:39.730 it that way if first time you write this 00:19:41.94000:19:41.950 you say why did that negative sign show 00:19:45.50900:19:45.519 up it's confusing it is confusing but go 00:19:48.53900:19:48.549 slow and not be confused here's another 00:19:51.81000:19:51.820 thing what we do is we often jump 00:19:53.94000:19:53.950 between a little infinitesimally mount 00:19:56.70000:19:56.710 of heat transfer in a small 00:19:58.35000:19:58.360 length or the area of the heat exchanger 00:20:01.44000:20:01.450 and then we go to the global heat 00:20:03.87000:20:03.880 transfer so we could say Q what's cute 00:20:07.05000:20:07.060 the total amount or the total rate of 00:20:10.35000:20:10.360 heat transfer from the hot into the cold 00:20:14.22000:20:14.230 fluid you could write that like the mass 00:20:17.19000:20:17.200 flow rate of the hot fluid specific heat 00:20:19.53000:20:19.540 of the hot fluid times the temperature 00:20:22.47000:20:22.480 of the hot in minus temperature of the 00:20:25.59000:20:25.600 hot out is that right or wrong do you 00:20:28.98000:20:28.990 agree with that how did we get that 00:20:32.27000:20:32.280 right a control volume just for the hot 00:20:36.75000:20:36.760 fluid and think about the Q the rate of 00:20:42.42000:20:42.430 heat transfer coming out of that control 00:20:44.37000:20:44.380 volume which includes only the hot fluid 00:20:47.63000:20:47.640 do this now look at a control volume 00:20:51.51000:20:51.520 only for the cold fluid and think about 00:20:54.87000:20:54.880 the same positive Q but not coming out 00:20:57.54000:20:57.550 of the cold fluid but positive going 00:21:00.60000:21:00.610 into the cold fluid and write the energy 00:21:02.82000:21:02.830 balance first law of thermo one for that 00:21:06.65000:21:06.660 would you get the same Q this is 00:21:09.48000:21:09.490 positive this is positive it's the same 00:21:11.46000:21:11.470 Q same rate of heat transfer the mass 00:21:14.31000:21:14.320 flow rate of the cold fluid the specific 00:21:16.68000:21:16.690 heat constant pressure of the cold fluid 00:21:22.34000:21:22.350 temperature cold out minus temperature 00:21:25.05000:21:25.060 cold in good and there's one more rate 00:21:29.43000:21:29.440 equation we're gonna drive it if I have 00:21:31.14000:21:31.150 time today which would say Q is equal to 00:21:34.38000:21:34.390 and it's the cousin of this one can you 00:21:36.69000:21:36.700 see that like these this is like version 00:21:39.51000:21:39.520 a and version a differential overall 00:21:44.72000:21:44.730 version B differential version B overall 00:21:48.99000:21:49.000 this is version C differential version C 00:21:52.65000:21:52.660 over all guess what that's going to be 00:21:54.18000:21:54.190 it's gonna look like this well I should 00:21:57.03000:21:57.040 have done this instead of an H I should 00:21:58.68000:21:58.690 have put au there shouldn't I you has 00:22:01.68000:22:01.690 the same units of H and sometimes I'll 00:22:03.42000:22:03.430 slip and I'll put an H there when I mean 00:22:05.16000:22:05.170 to put au it'll be you a times Delta TLM 00:22:12.81000:22:12.820 and that's a rate equation each of these 00:22:17.08000:22:17.090 three equations ABC have the same cute 00:22:19.90000:22:19.910 they're all positive it's the rate of 00:22:22.36000:22:22.370 heat transfer from the hot to the cold I 00:22:24.01000:22:24.020 hope I'm not beating something you know 00:22:25.66000:22:25.670 to death here it's like come on 00:22:27.22000:22:27.230 professor move on right okay we got it 00:22:30.25000:22:30.260 straight ready for a clicker question oh 00:22:35.67000:22:35.680 lo look at that how come it doesn't 00:22:37.99000:22:38.000 cover that up that's supposed to cover 00:22:40.48000:22:40.490 that up why is that not covering it up 00:22:45.66000:22:45.670 well I don't have time to figure out why 00:22:48.07000:22:48.080 it's not covering it up but which 00:22:50.56000:22:50.570 equation is not correct and when I asked 00:22:54.91000:22:54.920 this question at the Leben o'clock I did 00:22:56.77000:22:56.780 not have perfect score so you got 30 00:23:00.88000:23:00.890 seconds which of these four equations is 00:23:04.84000:23:04.850 incorrect now I forgot to mention 00:23:06.28000:23:06.290 something this equation C cap see right 00:23:10.21000:23:10.220 here is this rule that out it's not that 00:23:13.90000:23:13.910 one cap C is a heat capacity rate which 00:23:16.72000:23:16.730 is a mass flow-rate tons of specific 00:23:18.82000:23:18.830 heat up to hot fluid only three choices 00:23:23.32000:23:23.330 for you today polling has stopped well 00:23:29.92000:23:29.930 are we 100% correct 00:23:33.81000:23:33.820 good job good job good job good job and 00:23:38.35000:23:38.360 what was the error the thing I'm trying 00:23:41.14000:23:41.150 to harp on you can easily have a minus 00:23:43.27000:23:43.280 sign error and I'm talking about a 00:23:46.06000:23:46.070 positive Q from the hot to the cold and 00:23:49.00000:23:49.010 when you look from the perspective of 00:23:51.16000:23:51.170 the cold it's the cold in no no it's the 00:23:55.15000:23:55.160 cold out - the cold in so that was the 00:24:00.76000:24:00.770 incorrect thank you very much well as 00:24:05.20000:24:05.210 you could tell we get tired of writing 00:24:06.67000:24:06.680 to m dot C so P for either the cold 00:24:09.76000:24:09.770 fluid or the hot fluid and so when you 00:24:11.56000:24:11.570 get tired of something you just 00:24:12.87000:24:12.880 abbreviate it and so it's caps e cap C 00:24:16.09000:24:16.100 is called the heat capacity rate we're 00:24:18.07000:24:18.080 gonna have the heat capacity rate for 00:24:19.57000:24:19.580 the cold fluid as well as the heat 00:24:21.46000:24:21.470 capacity rate for the hot fluid you 00:24:24.04000:24:24.050 ready for a clicker question 00:24:25.94000:24:25.950 alright let's answer this one what are 00:24:31.16000:24:31.170 the SI units for the heat capacity rate 00:24:34.70000:24:34.710 cap si is it kilojoules kilojoules per 00:24:38.96000:24:38.970 Kelvin kilowatts kilowatts per Kelvin or 00:24:42.41000:24:42.420 something else other well probably a lot 00:24:50.69000:24:50.700 of people are trying to do this in their 00:24:52.34000:24:52.350 head what are the what is SI units for 00:24:54.44000:24:54.450 mass flow-rate 00:24:56.23000:24:56.240 kilogram per second what are the SI 00:24:59.30000:24:59.310 units for specific heat exactly 00:25:03.80000:25:03.810 kilojoules per kilogram degree C or 00:25:07.43000:25:07.440 Kelvin either one right and so I asked 00:25:11.12000:25:11.130 the same question no I don't have time 00:25:13.10000:25:13.110 you just cancel the kilograms 00:25:16.33000:25:16.340 what's a kilojoule kilowatt exactly 00:25:22.55000:25:22.560 kilowatt so what's the best answer isn't 00:25:27.62000:25:27.630 that the best answer all right 00:25:35.94000:25:35.950 now if we take a look at the same simple 00:25:39.14900:25:39.159 concentric tube or double pipe heat 00:25:41.91900:25:41.929 exchanger but we go with the more common 00:25:44.11000:25:44.120 counter flow configuration let's 00:25:46.60000:25:46.610 describe that so what we have is think 00:25:48.76000:25:48.770 about the hot fluid on one side and it's 00:25:52.02900:25:52.039 gonna go I'm gonna show the hot fluid 00:25:53.89000:25:53.900 coming in temperature hot in and then 00:25:56.71000:25:56.720 the temperature hot out but it's a 00:25:59.01900:25:59.029 counter flow so where do we bring the 00:26:01.51000:26:01.520 cooler fluid in the other way the 00:26:04.41900:26:04.429 temperature cold in comes here and the 00:26:08.11000:26:08.120 temperature cold out is on that other 00:26:10.65900:26:10.669 end and now you can you can see what 00:26:14.28900:26:14.299 does this give us in this case is it 00:26:17.64900:26:17.659 possible to get the temperature of the 00:26:19.84000:26:19.850 hot out lower than the temperature of 00:26:23.28900:26:23.299 the cold out it is and that's why we 00:26:27.54900:26:27.559 like it that's very common configuration 00:26:30.07000:26:30.080 so we'll plot temperature and then we'll 00:26:33.39900:26:33.409 plot X and we'll go from 0 to L like 00:26:38.01900:26:38.029 that and we'll show the temperature hot 00:26:41.11000:26:41.120 in as fixed and the temperature cold in 00:26:45.70000:26:45.710 over here is fixed and now you could 00:26:48.82000:26:48.830 sketch a number of different temperature 00:26:50.59000:26:50.600 profiles it would be more linear less 00:26:54.65900:26:54.669 you could have more of a constant delta 00:26:57.63900:26:57.649 T through that heat exchanger 00:26:59.47000:26:59.480 hence the profiles would be more flat 00:27:03.07000:27:03.080 and more straight lines okay instead of 00:27:05.94000:27:05.950 exponential shape like this would be the 00:27:08.44000:27:08.450 direction and this okay as I've shown it 00:27:12.63900:27:12.649 in this illustration is the hot out less 00:27:16.00000:27:16.010 than the cold out as for this problem 00:27:19.06000:27:19.070 yeah yeah so we see that that's very 00:27:21.90900:27:21.919 good I encourage you we're gonna get 00:27:24.49000:27:24.500 into some brutal math and then people oh 00:27:26.56000:27:26.570 I just have to solve problems on exams 00:27:28.60000:27:28.610 I'm just gonna focus on the math and I 00:27:30.51900:27:30.529 don't care about the physics or the 00:27:31.93000:27:31.940 intuition don't do that 00:27:33.25000:27:33.260 because what you'll need to have is 00:27:35.64900:27:35.659 intuition but there's plenty of 00:27:37.38900:27:37.399 questions that you can ask and challenge 00:27:39.73000:27:39.740 yourself and say okay for this type of 00:27:41.64900:27:41.659 Pete exchanger for a counterflow 00:27:43.96000:27:43.970 concentric tube heat exchanger and I can 00:27:46.72000:27:46.730 just substitute in a 00:27:47.98000:27:47.990 whole bunch of these and just make 00:27:49.48000:27:49.490 questions what happens if the you what 00:27:52.96000:27:52.970 is you again I forgot the name of you 00:27:55.77000:27:55.780 overall heat transfer coefficient for 00:27:58.36000:27:58.370 that heat exchanger it accounts for the 00:27:59.89000:27:59.900 convection the wall the convection on 00:28:03.10000:28:03.110 the inside outside and the conduction 00:28:04.93000:28:04.940 resistance through the wall right what 00:28:07.15000:28:07.160 happens if that goes up what happens 00:28:09.73000:28:09.740 that if the in if the overall heat 00:28:12.54900:28:12.559 transfer coefficient comes up but I 00:28:14.59000:28:14.600 don't change mass flow rates I don't 00:28:16.45000:28:16.460 change Inlet temperatures I don't change 00:28:18.49000:28:18.500 specific heats what happens to I don't 00:28:21.73000:28:21.740 know Q or temperature the cold out or 00:28:25.03000:28:25.040 something like that do you want to play 00:28:27.37000:28:27.380 this game for a few these you want to 00:28:30.52000:28:30.530 try this one so if somehow you goes up 00:28:36.58000:28:36.590 without changing the fluids the fluid 00:28:39.04000:28:39.050 flow rates the inlet temperatures what 00:28:41.83000:28:41.840 happens to Q 00:28:54.26000:28:54.270 well the queue will increase that's the 00:28:56.72000:28:56.730 right answer 00:28:57.38000:28:57.390 I'm glad a lot of us had it what does 00:28:59.90000:28:59.910 you represent a large u is like a large 00:29:05.18000:29:05.190 convection coefficient a large value of 00:29:07.82000:29:07.830 U means it's pretty easy to transfer the 00:29:10.40000:29:10.410 heat between the hot and the cold fluid 00:29:12.64000:29:12.650 so it'll be easier to you'll get more 00:29:15.74000:29:15.750 for the same size a heat exchanger etc 00:29:18.08000:29:18.090 somebody says I'd like to see that an 00:29:19.61000:29:19.620 equation well you probably want to look 00:29:21.04900:29:21.059 at an equation like our rate equation u 00:29:23.84000:29:23.850 a and then some delta T log mean and 00:29:26.87000:29:26.880 really what you did was you boost it up 00:29:28.73000:29:28.740 you I know that that's gonna have an 00:29:32.21000:29:32.220 effect on the outlet temperatures but 00:29:34.18000:29:34.190 but then this would go up the primary 00:29:37.54900:29:37.559 effect would be increasing Q well I 00:29:40.58000:29:40.590 don't have a lot of time to play with 00:29:42.11000:29:42.120 more of these but we could play with 00:29:43.66900:29:43.679 them maybe we'll come back to them again 00:29:45.53000:29:45.540 it's really a good way I think to get a 00:29:48.50000:29:48.510 grasp before you get bogged down in the 00:29:50.99000:29:51.000 mathematics a lot of times we have heat 00:29:54.38000:29:54.390 exchangers and one fluids either boiling 00:29:57.62000:29:57.630 or evaporating and one or one food could 00:30:00.53000:30:00.540 be condensing that's very common in heat 00:30:03.35000:30:03.360 exchangers think about refrigerants in 00:30:06.11000:30:06.120 evaporators the refrigerant is 00:30:08.53000:30:08.540 evaporating or boiling in that 00:30:10.51000:30:10.520 evaporator in our how about on the 00:30:13.82000:30:13.830 condenser outside the house the 00:30:15.91900:30:15.929 refrigerant is condensing in the 00:30:17.96000:30:17.970 condenser so it's very very common to 00:30:20.60000:30:20.610 have that well we like to work 00:30:23.65000:30:23.660 mathematically with this cap see this 00:30:26.41900:30:26.429 heat capacity rate which is the mass 00:30:28.13000:30:28.140 flow rate times a specific heat constant 00:30:30.56000:30:30.570 pressure what would be an effective not 00:30:34.85000:30:34.860 a true specific heat but what would be 00:30:39.32000:30:39.330 mathematically an effective specific 00:30:41.48000:30:41.490 heat if a fluid if the fluid is either 00:30:44.15000:30:44.160 evaporating or condensing that happens 00:30:47.93000:30:47.940 often in heat exchangers so what do we 00:30:49.88000:30:49.890 do is we go back and say what is our 00:30:51.62000:30:51.630 definition of specific heat constant 00:30:56.21000:30:56.220 pressure 00:30:56.66000:30:56.670 do you remember thermodynamics 00:31:01.74000:31:01.750 the rate of change of H with respect to 00:31:05.74000:31:05.750 T holding pressure constant H represents 00:31:11.59000:31:11.600 the property and thal P okay a little 00:31:16.87000:31:16.880 quick review is sisa P equal to C sub B 00:31:20.74000:31:20.750 for liquid is C sub P equal to C sub B 00:31:28.75000:31:28.760 for an ideal gas note is the correct 00:31:34.72000:31:34.730 answer for the second question and yes 00:31:38.83000:31:38.840 is the correct answer for the first 00:31:40.30000:31:40.310 question what's the difference between a 00:31:42.40000:31:42.410 liquid it's incompressible and an ideal 00:31:46.03000:31:46.040 gas it's very compressible and what's 00:31:49.00000:31:49.010 the relationship just as a review from 00:31:50.92000:31:50.930 thermodynamics C sub P and C sub B for 00:31:53.38000:31:53.390 an ideal gas isn't it are ya 00:31:57.40000:31:57.410 C sub E Plus R is equal to C sub P for a 00:31:59.89000:31:59.900 true ideal yes okay now what we'll do is 00:32:03.97000:32:03.980 play a little conceptual game of putting 00:32:07.21000:32:07.220 a constant pressure if you want to go 00:32:08.71000:32:08.720 back to thermo and be something like 00:32:10.45000:32:10.460 this here's a constant weight piston in 00:32:14.02000:32:14.030 a gravitational field and I have my 00:32:16.33000:32:16.340 fluid it's trapped in here and I'm going 00:32:19.24000:32:19.250 to just play conceptually the game of 00:32:21.25000:32:21.260 adding some heat I'm gonna add a little 00:32:24.01000:32:24.020 heat look at it cattle Italy it's 00:32:26.20000:32:26.210 constant pressure at all times I'm 00:32:27.70000:32:27.710 looking add a little heat that a little 00:32:29.65000:32:29.660 heat and I'm gonna plot it in a little 00:32:32.05000:32:32.060 bit of a funny way but let's go ahead 00:32:33.67000:32:33.680 and plot it like this where as we add 00:32:36.61000:32:36.620 the heat something's going to go up 00:32:38.71000:32:38.720 because I'm looking at derivative of 00:32:40.65000:32:40.660 enthalpy with respect to temperature 00:32:42.76000:32:42.770 let's put temperature on the x-axis and 00:32:45.09000:32:45.100 enthalpy on the y-axis I know it's a 00:32:48.37000:32:48.380 little different I'm sure I showed this 00:32:51.37000:32:51.380 to you when I taught thermo one or 00:32:53.05000:32:53.060 thermo two but I'll start it at 20 00:32:55.75000:32:55.760 degrees and I'll boost it to 40 degrees 00:32:57.88000:32:57.890 how did I get it to go from 20 degrees C 00:33:00.10000:33:00.110 to 40 degrees C water I'm gonna do this 00:33:02.83000:33:02.840 for water that's a fluid you're very 00:33:05.02000:33:05.030 comfortable with at 1 atm pressure right 00:33:08.01000:33:08.020 what happens when I do that does 00:33:10.45000:33:10.460 enthalpy of the water change at all it 00:33:13.93000:33:13.940 goes up a little 00:33:14.77000:33:14.780 how about at 180 mi go from 40 to 60 60 00:33:19.36000:33:19.370 to 80 00:33:19.93000:33:19.940 I hit something magical at 100 degrees C 00:33:23.34000:33:23.350 it's become saturated liquid exactly 00:33:26.86000:33:26.870 before that it was all sub cooled liquid 00:33:29.37000:33:29.380 but what's happening is I'm going up the 00:33:35.86000:33:35.870 enthalpies climbing and then we hit this 00:33:38.50000:33:38.510 in this value of enthalpy is H of F or H 00:33:42.82000:33:42.830 of G I can't remember H of F for 00:33:46.03000:33:46.040 saturated liquid now I continue to play 00:33:49.57000:33:49.580 the game of pumping it a little more q 00:33:52.20000:33:52.210 is the temperature gonna go up nah not 00:33:58.75000:33:58.760 immediately what happens it goes from 00:34:01.06000:34:01.070 saturated liquid a little bit turns into 00:34:03.07000:34:03.080 saturated vapor you hold it 1 bar that's 00:34:07.03000:34:07.040 what that little wait is that constant 00:34:09.97000:34:09.980 wait piston on the top does what expands 00:34:13.21000:34:13.220 dramatically as well so what happens to 00:34:17.26000:34:17.270 the H does the H go up the temperature 00:34:19.12000:34:19.130 is not changing but I'm keeping and 00:34:20.91900:34:20.929 dumping in energy Q is coming in T was 00:34:23.86000:34:23.870 coming in until I get up to H of 00:34:27.36000:34:27.370 saturated and now if I add anymore heat 00:34:31.51000:34:31.520 to it it's impossible no no you can add 00:34:34.18000:34:34.190 Heat what's gonna happen to the 00:34:36.25000:34:36.260 saturated vapor goes to superheated 00:34:39.49000:34:39.500 vapor and then the enthalpy will go up 00:34:42.52000:34:42.530 but the temperature go up you'll go to 00:34:44.35000:34:44.360 120 140 160 180 you can get saturated 00:34:49.38900:34:49.399 vapor quite hot and it'll just march 00:34:52.12000:34:52.130 right on up like that where is the 00:34:56.16900:34:56.179 specific heat constant pressure for the 00:34:58.99000:34:59.000 liquid water anywhere in this diagram 00:35:04.29000:35:04.300 isn't that it isn't it the slope of that 00:35:07.36000:35:07.370 line the definition how does DHD T at 00:35:10.78000:35:10.790 constant P isn't it the slope so what is 00:35:14.14000:35:14.150 C sub P for liquid water the slope of 00:35:16.81000:35:16.820 that line will be about 4.2 kilojoules 00:35:20.86000:35:20.870 per kilogram Kelvin maybe you remember 00:35:24.91000:35:24.920 that value how about the slope of this 00:35:27.10000:35:27.110 line 00:35:28.15000:35:28.160 see soapy water but it's in the vapor 00:35:30.78900:35:30.799 phase it's around 2.1 kilojoules per 00:35:36.49000:35:36.500 kilogram kelvin true good review now we 00:35:41.52900:35:41.539 have time for a clicker question you 00:35:43.27000:35:43.280 ready let's try it hopefully we're 00:35:47.14000:35:47.150 getting a lot right what is the 00:35:50.23000:35:50.240 effective specific heat for a fluid that 00:35:53.02000:35:53.030 is evaporating where is it evaporating 00:35:56.02000:35:56.030 anywhere in this diagram where it goes 00:36:00.06900:36:00.079 from set this point right here what is 00:36:04.21000:36:04.220 that point right there saturated liquid 00:36:07.29900:36:07.309 to saturated vapor where is it 00:36:11.20000:36:11.210 evaporating all right so let me start 00:36:13.90000:36:13.910 the timer what is the effective specific 00:36:18.52000:36:18.530 heat for a fluid that is evaporating all 00:36:25.08900:36:25.099 right so we're stopped you go back and I 00:36:27.67000:36:27.680 just was trying to emphasize the slope 00:36:30.22000:36:30.230 of the line on an enthalpy temperature 00:36:32.98000:36:32.990 diagram is the specific heat the cease 00:36:37.15000:36:37.160 of P for the liquid is the slope of the 00:36:39.37000:36:39.380 line the slope of the line what's the 00:36:41.58900:36:41.599 slope of this line infinity is infinity 00:36:54.99000:36:55.000 it's infinity 00:36:57.58000:36:57.590 all right now I'm gonna ask this is a 00:37:00.94000:37:00.950 below-the-belt question I'm just gonna 00:37:03.04000:37:03.050 ask it and I'll explain it but I don't 00:37:05.50000:37:05.510 think a lot of people get it right all 00:37:07.54000:37:07.550 right all right good you want a 00:37:09.28000:37:09.290 challenge huh all right here's a 00:37:11.83000:37:11.840 challenge for those that think my 00:37:13.45000:37:13.460 questions are too easy and too kind and 00:37:15.64000:37:15.650 all that what is the effective specific 00:37:18.91000:37:18.920 heat for a fluid that is condensing and 00:37:23.17000:37:23.180 we start the timer all done now let me 00:37:30.70000:37:30.710 ask this question it's it's cousin 00:37:32.44000:37:32.450 question right 00:37:33.70000:37:33.710 I have liquid water and I'm going to be 00:37:36.88000:37:36.890 heating the liquid water and I'm at the 00:37:39.67000:37:39.680 temperature of 50 degrees C where would 00:37:42.43000:37:42.440 that be on this diagram right here and 00:37:44.47000:37:44.480 I'm gonna heat it up to 60 degrees C 00:37:46.78000:37:46.790 when I heat the liquid or water from 50 00:37:49.75000:37:49.760 to 60 degrees C maybe I use a specific 00:37:52.78000:37:52.790 heat a value of the specific heat would 00:37:55.18000:37:55.190 be 4.2 kilojoules per kilogram Kelvin 00:37:58.39000:37:58.400 true I now want to cool liquid water 00:38:02.64000:38:02.650 from 60 back to 50 what is the specific 00:38:07.12000:38:07.130 heat for the liquid water when I'm 00:38:09.76000:38:09.770 cooling it from 60 down to 50 00:38:12.73000:38:12.740 it was 4.2 kilojoules per kilogram 00:38:16.39000:38:16.400 Kelvin on the heating is it negative 4.2 00:38:21.73000:38:21.740 kilojoules per kilogram on the cooling 00:38:25.92000:38:25.930 isn't this a tough question let's do the 00:38:30.82000:38:30.830 same thing for the vapor I'm out here 00:38:33.25000:38:33.260 somewhere in the vapor and I 00:38:34.78000:38:34.790 conceptually heated up I have a positive 00:38:37.00000:38:37.010 specific heat a positive delta T a 00:38:39.94000:38:39.950 positive Q coming in all I have is 00:38:43.12000:38:43.130 cooling it down I have still a positive 00:38:45.31000:38:45.320 specific heat I have a negative delta T 00:38:48.31000:38:48.320 and a negative Q you want to try that 00:38:52.72000:38:52.730 question again same question what is the 00:38:56.50000:38:56.510 effective specific heat of a fluid that 00:38:58.72000:38:58.730 is condensing 00:39:08.98000:39:08.990 well let's just grade it 00:39:11.21000:39:11.220 I don't know how to explain it any 00:39:12.86000:39:12.870 better right isn't that true it's 00:39:17.66000:39:17.670 infinity positive infinity and let's go 00:39:24.35000:39:24.360 back to the previous how do I do that 00:39:26.66000:39:26.670 this one look at that the class is 00:39:29.93000:39:29.940 learning very good well I'm out of time 00:39:36.77000:39:36.780 but next time there's a thick derivation 00:39:39.32000:39:39.330 that I want to get into but it's in the 00:39:41.60000:39:41.610 book and so please read the book thank 00:39:44.03000:39:44.040 you very much
Office location
Engineering company LOTUS®
Russia, Ekaterinburg, Lunacharskogo street, 240/12