00:01
For part a.
00:02
In an isothermal process involving an ideal gas, the work done on the gas, w, would be equalling the negative work in the environment.
00:11
This would be equalling negative nrt times the natural log of the final volume divided by the initial volume.
00:21
And this is, again, isothermal process with an ideal gas.
00:37
From this when the temperature is constant however the ideal gas law is then pressure initial volume initial equaling pressure final volume final and this is equalling nrt when the temperature is constant and so we we can rewrite the work done on the gas this would be equalling the negative initial pressure initial volume multiplied by the natural log of the final volume divided by the initial volume.
01:10
So this would be equalling negative 10 to the third pascal's multiplied by 0 .50 square or rather cubic meters multiplied by the natural log of 1 .25 cubic meters divided by again 0 .5 .00 cubic meters.
01:34
And we find that the work done is then equaling negative 4 .58 times 10 to the fourth joules, the fact that this is negative means that the gas is doing work on the environment.
01:49
Now, for part b, we have simply the first law of thermodynamics where the change in the internal energy is equaling the work minus, rather the work plus the heat transfer plus the work.
02:06
My apologies...