# Calculate change in entropy when both temperature and volume change

Calculate the change in entropy when $$\pu{23.5 g}$$ of oxygen gas is heated from $$\pu{240 K}$$ to $$\pu{360 K}$$ in such a way that its pressure increases from $$\pu{2.00 kPa}$$ to $$\pu{8.00 kPa}.$$ Assume ideal behavior.

I have attempted this problem for quite a long time, but to no avail. My approach is to use the fact that entropy is a state function, and break the question into smaller pieces.

1. Isothermal reversible compression from $$\pu{2.00 kPa}$$ to $$\pu{8.00 kPa}$$ (temperature remains $$\pu{240 K}$$).
2. Heating from $$\pu{240 K}$$ to $$\pu{360 K}$$ at constant pressure ($$\pu{8.00 kPa}$$).

In step 1,

$$\Delta S_1 = nR\ln\left(\frac{P_1}{P_2}\right) = \pu{-8.47 J K-1}$$

In step 2,

$$\Delta S_2 = nC_p\ln\left(\frac{T_2}{T_1}\right) = \frac{7}{2}nR\ln\left(\frac{T_2}{T_1}\right) = \pu{8.67 J K-1}$$

Therefore, in total

$$\Delta S_\mathrm{tot} = \pu{-8.47 J K-1} + \pu{8.67 J K-1} = \pu{0.200 J K-1}$$

However, the answer key uses a constant volume heating (rather than a constant pressure heating), and claims an answer of $$\pu{-2.27 J K-1}.$$

• I used constant volume heating and constant temperature volume change, and I confirm you answer. – Chet Miller Jun 25 at 2:45