1 00:00:13,490 --> 00:00:16,360 [noise] Welcome back. Ah in this particular [vocalized-noise] 2 00:00:16,360 --> 00:00:21,910 lecture we are going to cover ah review the fundamentals of the first, ah fundamentals 3 00:00:21,910 --> 00:00:29,750 of the 0th ah [vocalized-noise] law of thermodynamics ah temperature, ah basics for calculating 4 00:00:29,750 --> 00:00:34,170 temperature. And we will discuss about pressure and some of the devices which are typically 5 00:00:34,170 --> 00:00:39,320 used to ah find out pressure or pressure differences. So, this is our learning objective ok. So, 6 00:00:39,320 --> 00:00:43,550 let me just go through the first the ah 0th law of thermodynamics; obviously, ah you all 7 00:00:43,550 --> 00:00:48,830 are [vocalized-noise] know this concept very well, but just to summarize. So, ah what we 8 00:00:48,830 --> 00:00:53,680 say about 0th law of thermodynamics is that ah if 2 bodies are in thermal equilibrium 9 00:00:53,680 --> 00:00:59,110 with the third body, they are also in thermal equilibrium with each other. And ah in other 10 00:00:59,110 --> 00:01:06,320 word you can replace the third body by a thermometer. And thus your 0th law can be restated as 2 11 00:01:06,320 --> 00:01:10,820 bodies a in thermal equilibrium if both have the same temperature reading even if they 12 00:01:10,820 --> 00:01:14,930 are not in contact. So, that is become the basically the 0th law 13 00:01:14,930 --> 00:01:20,369 of thermodynamics. Now practically ah it means that ah we need to ah understand how the termometers 14 00:01:20,369 --> 00:01:27,259 work ok. Now all the temperature scale, which ah has been devised are based on some easily 15 00:01:27,259 --> 00:01:33,899 reproducible state ok. And the states is basically ice point [noise] and steam point. So, basically 16 00:01:33,899 --> 00:01:40,329 0 degree and 100 degree ok. So, the point is that you can consider any particular fluid, 17 00:01:40,329 --> 00:01:44,189 and you can scale it in such a way that you get 0 degree and 100 degree. 18 00:01:44,189 --> 00:01:52,060 But the point between 0 to 100, if not ah even if you calibrate ah only the 0 and 100 19 00:01:52,060 --> 00:01:58,409 the other points may differ. The reason being that the thermal expansivity of the fluid 20 00:01:58,409 --> 00:02:05,880 vary from each other. And that is why such a thermometer or not commonly used. The one 21 00:02:05,880 --> 00:02:12,180 which is used is basically based on either ah idle gas thermometer, which is which shows 22 00:02:12,180 --> 00:02:20,160 that ah it is independent of gases which are considered. And the scale is a linear as a 23 00:02:20,160 --> 00:02:23,630 function of a temperature in other word the pressure is linear as a functional temperature 24 00:02:23,630 --> 00:02:27,200 [vocalized-noise] ok. And thus, you can change the gas and still 25 00:02:27,200 --> 00:02:32,150 ah you can achieve ah ah the same points and you can still calibrate it well [vocalized-noise]. 26 00:02:32,150 --> 00:02:37,880 Or the same thing which you can use in idle gas thermometer is by considering absolute 27 00:02:37,880 --> 00:02:42,890 temperature scale, which is based on second law of thermodynamics. And both are equivalent, 28 00:02:42,890 --> 00:02:46,530 ah it can be shown. So, in case of a absolute thermodynamic scale 29 00:02:46,530 --> 00:02:52,030 or thermodynamic temperature scale the examples are kelvin and Rankine ah scale ok. Now, pressure 30 00:02:52,030 --> 00:02:57,060 of course, pressure we all know is it is a normal force per unit area, it is typically 31 00:02:57,060 --> 00:03:05,140 used for gas and liquid. We do not use the pressure for solid, ah we use ah stress ah 32 00:03:05,140 --> 00:03:13,010 normal stress for solids. And a unit depending on the SI unit is this, other units are given 33 00:03:13,010 --> 00:03:19,820 here [vocalized-noise]. Now it is very clear that ah the pressure executed or felt by the 34 00:03:19,820 --> 00:03:26,570 feet of a chubby person is substantially larger than that for slim person ok [vocalized-noise]. 35 00:03:26,570 --> 00:03:33,380 Now, what is variation of pressure? Now, fluid or pressure for fluid at rest does not change 36 00:03:33,380 --> 00:03:38,510 in the horizontal direction ok. So, that means, there is no ah once it is at rest because 37 00:03:38,510 --> 00:03:42,790 there is no flow. So, the force is along the horizontal directions are going to be constant 38 00:03:42,790 --> 00:03:52,690 ok. So, this pressure [noise], and this pressure [noise] if at rest is going to be same ok. 39 00:03:52,690 --> 00:03:59,450 Now, let us consider a rectangular ah rectangular region; which is this ok. And then do a simple 40 00:03:59,450 --> 00:04:05,720 force balance for this particular mass within the rectangular element. So, the force balance 41 00:04:05,720 --> 00:04:11,490 should be because it is not flowing should be 0. So, which means this is basically the 42 00:04:11,490 --> 00:04:22,509 force acting on it ok, on this from below. This is the force [noise] due to the air ok, 43 00:04:22,509 --> 00:04:28,990 or due to the ah [vocalized-noise] fluid above it acting on this particular element. And 44 00:04:28,990 --> 00:04:33,879 this is basically the mass or the weight of ah mass this is the weight multiplied by ah 45 00:04:33,879 --> 00:04:37,189 rho g multiplied by the volume, which is nothing but the weight [vocalized-noise]. So, if you 46 00:04:37,189 --> 00:04:43,001 do a simple mathematical ah calculation, and take it out the common term [noise]. What 47 00:04:43,001 --> 00:04:50,669 you get is nothing but that P 2 minus P 1 is nothing but minus rho g delta h. In other 48 00:04:50,669 --> 00:04:56,159 word, p below is more than p above by this value [noise] ok. 49 00:04:56,159 --> 00:05:03,780 So, the pressure increases linearly with ah [vocalized-noise] distance, ah as we go down 50 00:05:03,780 --> 00:05:10,960 ah in depth, because of the added [vocalized-noise] ah weight of the fluid. This also tells you 51 00:05:10,960 --> 00:05:18,150 that the pressure along the horizontal ah ah points for a given fluid will remain constant, 52 00:05:18,150 --> 00:05:24,979 though the pressure ah in depth increases. But this (Refer Time: 05:23) tells you that 53 00:05:24,979 --> 00:05:34,300 the pressure here, same as here, here, here, here, here and here. And pressure here and 54 00:05:34,300 --> 00:05:39,789 this are not same. For simple reason is this is a different fluid ok. So, you need to have 55 00:05:39,789 --> 00:05:46,159 the same fluid in order to have the ah equality of the pressure ok [vocalized-noise]. 56 00:05:46,159 --> 00:05:51,999 Now, what are the measurement devices for pressure? One is ah [vocalized-noise] the 57 00:05:51,999 --> 00:05:57,449 simplest one is the barometer; which is used for atmospheric pressure ok. So, for example, 58 00:05:57,449 --> 00:06:03,020 ah this is a simple device due to the vacuum the pressure here is this you can apply a 59 00:06:03,020 --> 00:06:09,009 force valence, and you can show that p atmosphere is nothing but the density of the fluid which 60 00:06:09,009 --> 00:06:14,400 we consider; which is nothing but the mercury, ah the g gravity and the height which is being 61 00:06:14,400 --> 00:06:19,650 ah which is ah rise [vocalized-noise] due to the pressure. And for one atmosphere this 62 00:06:19,650 --> 00:06:22,790 is nothing but 760-millimeter hg [vocalized-noise] ok. 63 00:06:22,790 --> 00:06:29,529 Now, it also tells you that the cross-sectional area of the tube has no effect on the the 64 00:06:29,529 --> 00:06:35,159 height of the the barometer. And even though you use different [vocalized-noise] column, 65 00:06:35,159 --> 00:06:41,530 the height will remain the same ok, because of the simple balance here. So, in addition 66 00:06:41,530 --> 00:06:46,460 to barometer we have also other devices. For example, if you are interested in ah measuring 67 00:06:46,460 --> 00:06:53,569 the pressure of a container ah having a gas, one can use fluid ah column to measure ah 68 00:06:53,569 --> 00:06:58,009 simple pressure difference, and that can be used ah to measure the pressure of the gas 69 00:06:58,009 --> 00:07:03,580 container ok. Otherwise fluid could be any fluid mercury water alcohol or oil. 70 00:07:03,580 --> 00:07:07,639 So, this is an example here. For example, if you are interested to find out the pressure 71 00:07:07,639 --> 00:07:13,309 of this gas. Since gas [vocalized-noise] is typically has very, very small density, compared 72 00:07:13,309 --> 00:07:20,409 to the heavier fluid [noise]. So, pressure here would be same as pressure P 1 [noise] 73 00:07:20,409 --> 00:07:25,449 ok. Now P 1 pressure because of the force balance this is not moving. The P 1 P 1 pressure 74 00:07:25,449 --> 00:07:29,240 here in this side and this side should be same, because of the force balance. So, P 75 00:07:29,240 --> 00:07:34,379 1 and P 2 should be same. So, and here is the p atmosphere ok. So now, 76 00:07:34,379 --> 00:07:45,569 you can simply use P 2 is equal to p atmosphere [noise] ok, plus the rho gh ok. So, this is 77 00:07:45,569 --> 00:07:49,009 a simple way to calculate. So, thus; that means, if you calculate P 2 you know exactly 78 00:07:49,009 --> 00:07:52,860 what is P 1. And that means, the gas of the container. 79 00:07:52,860 --> 00:07:59,009 Now, in addition to this ah you have manometer, which many times you stack up the fluid layers. 80 00:07:59,009 --> 00:08:06,119 And in this case, you have 3 fluids having these heights. And one can relate p pressure 81 00:08:06,119 --> 00:08:13,349 at 1 with respect to ah p atmosphere, and the density of the ah this fluid with different 82 00:08:13,349 --> 00:08:21,689 heights. So, one can simply use p atmosphere plus the rho 1 gh 1 plus rho 2 gh 2 plus rho 83 00:08:21,689 --> 00:08:29,189 3 g h 3. And this is exactly [noise] what has been done to achieve P 1 ok. One can also 84 00:08:29,189 --> 00:08:33,279 use differential manometer in order to find the pressure difference between 1 and 2. 85 00:08:33,279 --> 00:08:40,150 So, we can start from P 1 ok, and go down and the height, it does not matter what kind 86 00:08:40,150 --> 00:08:46,060 of geometry we are using, what we are interested is, it should be of same fluid and effectively 87 00:08:46,060 --> 00:08:55,100 the height of the from this point to whatever for example, this point. So, ah P 1 [noise] 88 00:08:55,100 --> 00:09:01,130 is this plus rho 1, which is the fluid here which we are interested to find the difference 89 00:09:01,130 --> 00:09:07,430 from this this 2 points. So, rho 1 g plus whatever the height from this point till a, 90 00:09:07,430 --> 00:09:11,870 which is nothing but a plus h and that is what you get rho 1 g a plus h. 91 00:09:11,870 --> 00:09:18,690 Now, this pa is same as whatever is at pb. So, we do not ah we we go from here to directly 92 00:09:18,690 --> 00:09:26,100 to here. And now we are going up in the direction ok. So, we are going to subtract the [vocalized-noise] 93 00:09:26,100 --> 00:09:32,690 the rho gh from this term. So, that will be rho 2. Because this is rho 2 g h here [noise]. 94 00:09:32,690 --> 00:09:39,320 Now from here to here we are going to subtract minus rho 1 g a and thus we are going to achieve 95 00:09:39,320 --> 00:09:44,880 find out the pressure at 2. So, if you readjust, this term we get p 1 96 00:09:44,880 --> 00:09:52,600 minus P 2 is is equal to rho 2 minus rho 1 gh. So that means, the pressure drop from 97 00:09:52,600 --> 00:09:59,959 here to here is equal to the difference in the density of this fluid which we of this 98 00:09:59,959 --> 00:10:03,860 with respect to rho 2. So, rho 2 minus rho 1. So, rho 2 is [vocalized-noise] usually 99 00:10:03,860 --> 00:10:09,800 is going to be much, much larger than rho 1 ok. So now, we can do a simple example here 100 00:10:09,800 --> 00:10:13,680 to to exercise this. A piece of experimental apparatus as shown 101 00:10:13,680 --> 00:10:23,880 in the figure below ok, is located where g is 9.5 meter per second square, and the temperature 102 00:10:23,880 --> 00:10:28,800 is 5-degree celsius. Air flow inside the apparatus is determined by measuring the pressure drop 103 00:10:28,800 --> 00:10:36,970 across an oriface, which is nothing but this ok. With a mercury manometer ok, and the density 104 00:10:36,970 --> 00:10:41,550 is equilibrium, showing a height difference of [noise]. 105 00:10:41,550 --> 00:10:52,019 So, this height [noise] is 200 millimeter ok. So, what is the pressure drop from ok 106 00:10:52,019 --> 00:10:55,580 across the [vocalized-noise] oriface. So, in the word what is the pressure drop? Let 107 00:10:55,580 --> 00:11:01,970 us say from here to here and ah. So, the pressure drop from 1 to 2 can be written as simply 108 00:11:01,970 --> 00:11:05,850 here, why because of course, the density of the air is extremely small, and this height 109 00:11:05,850 --> 00:11:13,350 difference does not will not bother. The density of air is close to 1.2 kg per meter cube ok. 110 00:11:13,350 --> 00:11:19,649 So now, we have done this exercise. Before that [vocalized-noise] that pressure p 1 minus 111 00:11:19,649 --> 00:11:26,110 p [noise] 2 is nothing but rho 2 [noise] minus rho 1 gh. So, ok rho 2 is of course, the density 112 00:11:26,110 --> 00:11:33,790 of the mercury rho 1 is density of the air. Now, this we can ignore also because ah 13, 113 00:11:33,790 --> 00:11:41,329 600 minus 1, 1.2 is going to be negligible. So, for measuring approximation we can simply 114 00:11:41,329 --> 00:11:48,970 write rho hgh, and this comes out to be this [noise] value ok ok. So, here we ignored rho 115 00:11:48,970 --> 00:11:56,041 1, and simply written rho gh hg, and thus [vocalized-noise] the value is ok. So, ah 116 00:11:56,041 --> 00:12:00,100 so, that will be the end of ah this lecture [noise]. So, where we discussed [vocalized-noise] 117 00:12:00,100 --> 00:12:05,310 very quickly the temperature concept ah, and as well as the pressure ok. So, we will see 118 00:12:05,310 --> 00:12:10,800 you next time ah, and where we are going to introduce ah rather review the energy conservation 119 00:12:10,800 --> 00:12:12,050 in the first law of thermodynamics [noise].