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 $\pu{-2.27 J K-1}.$

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

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