Equation for temperature change, 4F.11

Volume: $\Delta S = nR\ln \frac{V_{2}}{V_{1}}$
Temperature: $\Delta S = nC\ln \frac{T_{2}}{T_{1}}$

sonalivij
Posts: 70
Joined: Fri Sep 28, 2018 12:27 am

Equation for temperature change, 4F.11

During the test of an internal combustion engine, 3.00 L of nitrogen gas at 18.5° C was compressed suddenly (and irreversibly) to 0.500 L by driving in a piston. In the process, the temperature of the gas increased to 28.1°C. Assume ideal behavior. What is the change in entropy of the gas?

I know this problem has to be done in two steps - one with a change in volume and one with a change in temperature. For the second part, I tried to use the equation the textbook gave, deltaS=C*ln(T2/T1) for any change in enthalpy and using 5/2R as C because it is at constant volume for the second part and a linear molecule. This method had been used for an example in the textbook as well. I got .673 for this part. The solutions manual however used the equation deltaS=n*R*ln(T2/T1) and got .269. Why should we use this new equation and not the one with heat capacity?

paytonm1H
Posts: 74
Joined: Fri Sep 28, 2018 12:18 am

Re: Equation for temperature change, 4F.11

I just experienced the same thing. I don't understand why deltaS=nRln(T2/T1) is valid in this problem.

Laura Gong 3H
Posts: 89
Joined: Fri Sep 28, 2018 12:26 am
Been upvoted: 1 time

Re: Equation for temperature change, 4F.11

At least for the 6th edition, this particular question is 9.13 and on the website, the solution manual errors page says that the answer you got was correct because like you predicted, because N2 is a diatomic gas we need to use Cv=5/2R not 3/2R.

Ryan Danis 1J
Posts: 66
Joined: Fri Sep 28, 2018 12:18 am

Re: Equation for temperature change, 4F.11

I faced the same problem and was confused why I could get neither the equation in the solutions manual via manipulating other equations nor the answer in the book. Must be an error in the 7th edition solutions and solution manual unless anybody else has an explanation.

Theodore_Herring_1A
Posts: 60
Joined: Fri Sep 28, 2018 12:29 am

Re: Equation for temperature change, 4F.11

I, as well as many other posters on chemistry community, have faced the same problem. I believe it to be a solutions manual error, as we have never encountered that equation in lecture and it is not on the formula sheet.