Question

2 moles of an ideal monoatomic gas undergoes a reversible process for which $P^{2}V=$ constant. The gas sample is made to expand from an initial volume of $1L$ to a final volume of $4L$ starting from an initial temperature of $300K$. Find the value of $\Delta S_{sys}$ for the above process. Report your answer as 'X' where $\Delta S_{sys}=XRln2$

• A. 7
• B. 4
• C. 9
• D. 3

Answer 1

The correct option is A 7

$P^{2}V=constant$

$\therefore {\left(\frac{nRT}{V}\right)}^{2}V=constant$
$\therefore \frac{T^2}{V}=constant$
$\therefore \frac{T_1^2}{V_1}=\frac{T_2^2}{V_2}$

$\therefore \frac{{\left(300\right)}^2}{1}=\frac{T_2^2}{4}$
$\therefore T_2=600K$
$\Delta S_{sys}=n{C}_{V}ln\frac{T_2}{T_1}+nRln\frac{V_2}{V_2}$
$=2\times \frac{3R}{2}ln\left(\frac{600}{300}\right)+2\times Rln\left(\frac{4}{1}\right)=7Rln2$
$\therefore X=7$