Question

When one mole of an ideal gas is compressed to half its initial volume and simultaneously heated to twice to its initial temperature, the change in entropy $\left(\Delta S\right)$ is -

• A. $C_v$ In 2
• B. $C_p$ In 2
• C. R In 2
• D. $(C_v-R)$ In 2

Answer 1

The correct option is D $(C_v-R)$ In 2

Given,

No.of moles of Ideal gas =1 mole; n=1

Ideal gas compressed to half of its initial volume i.e, $V_1=1;V_2=\frac{1}{2}$

Ideal gas heated to twice to its initial temperature i.e, $T_1=1;T_2=2$

We know that, $\Delta S=n{C}_{v}ln\left(\frac{T_2}{T_1}\right)+nRln\left(\frac{V_2}{V_1}\right)$

$\Delta S=C_{v}ln\left(\frac{2}{1}\right)+Rln\left(\frac{1}{2}\right)$

$\Delta S=C_{v}ln\left(\frac{2}{1}\right)-Rln\left(\frac{2}{1}\right)$

$\Delta S=(C_v-R)ln2$