Please show all working 50 moles of an ideal gas initially...

'Please show all working: 50 moles of an ideal gas initially has volume of 0.8 m3 a pressure of 160 kPa, and temperature of 280 K: The volume of the gas increases to 1.2 m3 , while its pressure decreases to 80 kPa. At any temperature T , the internal energy of the gas is given by U = aT , where 500 ) K-1. During the expansion, the volume and pressure are related by V = AP + B_ where A and B are constants. Assuming that the expansion is reversible, calculate: (a) The values of the constants A and B_ b) The work done by the gas during the expansion. c) The heat absorbed by the gas during the expansion: (d The change in the entropy of the gas due to the expansion:'

Transcript

00:01 In this problem, we need to calculate four different parts based on the problem given to us.

00:04 So the problem is talking about expansion, which is reversible, and we have different equations in this problem along with the data.

00:11 So let us see what different data do we have.

00:14 So first of all, we can write that we have the value of b1, that is initial pressure.

00:18 So this will be equals to 160 kilo -pascal.

00:21 Then we have the number of moles in this equation that can be written as 50.

00:25 Then we have the value of v1 that is initial volume as 0 .8 meter cube.

00:31 Then we have the value of v2 that is final volume as 1 .2 meter cube.

00:36 Then we have the value of p2 that is final pressure equals to 80 kilopascal.

00:42 Now we need to calculate the value of t2.

00:45 Then only we can proceed with our different parts of this very problem.

00:49 So from ideal gas which is pv equals nrt we can say that nr will be equals to pv over nr pv over t so why we are substituting in this way because nr will remain constant before and after the reaction or whatever happening in the problem hence we can create one equation over here like p1 v1 over t1 and this one will be equals to p2 v2 over t2 now if we substitute the value and rearrange this equation a little bit we will get the value of t2 as 8 for t over 4 and this comes around 2 1 0 kelvin and this is the answer for t2 value that is final temperature now let us see the first part so in the first part we need to calculate the value of uh a and b as constants so first of all we have the initial conditions so we can write that ap 1 plus p will be our first equation because we have been given in the problem that there is an equation which is like v equals a p plus b now with this particular equation what will what will happen we can say that we have the value of we have the value of p1 so there is a very beautiful reaction with a and b so that will be 0 .8 equals a multiplied 160 plus b so now if we try to calculate at final condition so we can write that at final condition it will be like 1.

02:21 0 .2 equals 80 multiplied a and it will be plus b...

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