WEBVTT 00:00:00.000 --> 00:00:02.740 This is College Physics Answers with Shaun Dychko. 00:00:03.580 --> 00:00:05.780 One foot is standing on a ceramic tile 00:00:05.780 --> 00:00:07.600 and the other foot is standing on 00:00:07.600 --> 00:00:11.120 Sobel carpet and the top of the ceramic 00:00:11.120 --> 00:00:15.420 or wool is meant to be at a temperature of 33 degree Celsius 00:00:15.420 --> 00:00:17.420 or we are gonna call that T2 00:00:17.420 --> 00:00:23.960 because in our formula for thermal rate of thermal conduction, we have T2 00:00:24.000 --> 00:00:27.100 representing the body from which the heat 00:00:27.100 --> 00:00:30.820 leaves and it goes towards body one 00:00:30.820 --> 00:00:33.960 and so we have heat going from the top 00:00:33.960 --> 00:00:37.300 so that’s at the higher temperature so that's T2 00:00:37.300 --> 00:00:40.300 going towards the bottom of this thickness 00:00:40.300 --> 00:00:42.000 of ceramic or thickness of wool 00:00:42.000 --> 00:00:44.300 and the bottom is T1 and that's 00:00:44.340 --> 00:00:47.500 temperature 10 degree Celsius and so 00:00:47.500 --> 00:00:49.940 the question is at what rate must heat be 00:00:49.940 --> 00:00:50.980 be transferred from the foot 00:00:50.980 --> 00:00:52.980 to the top of the ceramic or wool, 00:00:52.980 --> 00:00:57.260 in order to maintain this 33 degree Celsius temperature 00:00:58.320 --> 00:01:01.120 and that'll be the same as the rate 00:01:01.120 --> 00:01:05.280 with which the top is losing energy 00:01:05.280 --> 00:01:10.520 to the bottom and so that's why we are calculating this. 00:01:10.520 --> 00:01:12.020 This is the rate at which energy is 00:01:12.020 --> 00:01:13.320 transferred from the top of the ceramic to 00:01:13.320 --> 00:01:15.320 the bottom of the ceramic. 00:01:15.320 --> 00:01:17.320 And so since the top is losing 00:01:17.320 --> 00:01:18.100 energy at that rate, 00:01:18.100 --> 00:01:21.840 it needs to gain that same rate of energy from the foot. 00:01:23.880 --> 00:01:26.620 Now the foot area is 80 square centimeters 00:01:26.620 --> 00:01:28.060 which we multiplied by one meter for every 00:01:28.060 --> 00:01:29.500 100 centimeters squared to get 00:01:29.500 --> 00:01:32.980 0.008 squared meters and the thickness is 00:01:32.980 --> 00:01:35.500 two centimeters which is two times ten to the minus two meters. 00:01:35.540 --> 00:01:38.500 Taking care always of unit conversions. 00:01:38.500 --> 00:01:40.620 In this step we rewrite down the information 00:01:40.620 --> 00:01:42.240 that we know so we don't have to think 00:01:42.240 --> 00:01:42.880 about this later. 00:01:44.300 --> 00:01:44.700 All right. 00:01:45.620 --> 00:01:49.620 So we have the rate of thermal energy conduction is the 00:01:49.660 --> 00:01:52.820 thermal conductivity of the material which in the case of ceramic 00:01:52.860 --> 00:01:55.280 we take to be that of concrete or brick 00:01:55.280 --> 00:01:58.800 0.84 Jules per second per meter per Celsius degree 00:01:58.800 --> 00:02:02.080 and the thermal connectivity of wall is 0.04. 00:02:03.640 --> 00:02:04.080 OK. 00:02:04.840 --> 00:02:06.920 So if thermal conductivity multiplied by area 00:02:06.920 --> 00:02:08.360 times the temperature difference divided by 00:02:08.360 --> 00:02:10.220 the thickness of a material and so 00:02:10.220 --> 00:02:12.700 we can substitute for all of these things except for K 00:02:12.700 --> 00:02:14.300 and to get a formula into which 00:02:14.300 --> 00:02:15.840 we just plug K for ceramic 00:02:15.880 --> 00:02:17.720 and then K for wool to get our answers. 00:02:18.180 --> 00:02:20.580 So if K times 0.008 squared meters 00:02:20.580 --> 00:02:23.180 times 33 degree Celsius minus 10 degree Celsius 00:02:23.180 --> 00:02:25.300 divided by two centimeters giving us K 00:02:25.300 --> 00:02:29.380 multiplied by this 9.2 meters Celsius degrees 00:02:29.380 --> 00:02:31.200 which are kind of nonsensical units 00:02:31.240 --> 00:02:34.360 but they are what works out from multiplying 00:02:34.360 --> 00:02:36.140 and dividing all these things and then 00:02:36.140 --> 00:02:39.240 when you multiply by K, it will end up being watts. 00:02:41.320 --> 00:02:44.200 So for ceramic the rate of heat transfer is 00:02:44.200 --> 00:02:48.640 going to be 0.84 Joules per second per meter per Celsius degree 00:02:48.640 --> 00:02:51.240 times 9.2 meter Celsius degrees 00:02:51.240 --> 00:02:53.240 and the meter and Celsius degrees cancel 00:02:53.240 --> 00:02:54.420 and sure enough the units are 00:02:54.420 --> 00:02:57.260 joules per second which is watts, 7.7 watts, 00:02:57.260 --> 00:03:00.280 of energy needs to be given to the top 00:03:00.280 --> 00:03:02.200 of the ceramic from the foot in order to 00:03:02.200 --> 00:03:03.860 maintain this rate of heat transfer 00:03:03.860 --> 00:03:06.080 across the thickness of the ceramic towards the bottom 00:03:07.240 --> 00:03:08.200 and then for the wool 00:03:08.200 --> 00:03:11.040 we plug in 0.04 instead of 0.84 00:03:11.040 --> 00:03:13.820 and we end up with 0.4 watts and so you can see 00:03:13.820 --> 00:03:15.980 the wool is a much better insulator 00:03:16.020 --> 00:03:19.520 due to its lower thermal conductivity 00:03:19.520 --> 00:03:20.840 and we are seeing that in this 00:03:20.840 --> 00:03:24.220 rate of heat transfer is much lower than that for ceramic.