Question

One mole of an ideal gas is expanded irreversibly from an initial pressure of $2$ atm to a final pressure of $1$ atm at a temperature of $300K$. Let qirr, $△S_{sys}$ and $△S_{surr}$ represent the magnitude of the heat transfer, the entropy change of the system, and the entropy change of the surrounding respectively. Assuming that the surrounding does not perform any work, the correct relation(s) is/are ($R$ is the universal gas constant).

• A. $△S_{surr}=-q_{rr}/300$
• B. $△S_{sys}=Rln2$
• C. $△S_{sys}=qirr/300$
• D. $qirr<300Rln2$

Answer 1

Answer: (A), (B), (D)

$△S_{surr}=-q_{rr}/300$
$qirr<300Rln2$
$△S_{sys}=Rln2$

$\Delta S_{sys}=n{C}_{V}ln\left(\frac{T_2}{T_1}\right)+nRln\left(\frac{V_2}{V_1}\right)=nRln\left(\frac{V_2}{V_1}\right)=nRln\left(\frac{P_1}{P_2}\right)\therefore \Delta S_{sys}=Rln2=\frac{q_{rev}}{T}\Delta S_{surr}=-\frac{Q_{irrev}}{T}\Delta S_{surr}=-\frac{q_{rev}}{300}$

Also, $q_{irr}<q_{rev}$

$\therefore q_{irr}<\Delta S_{sys}\times T\therefore q_{irr}<300Rln2$