Question

One mole of an ideal monoatomic gas at temperature $T_o$ expands slowly according to the law $\frac{P}{V}=constant$. If the final temperature is $2T_o$, heat supplied to the gas is:

• A. $2R{T}_o$
• B. $\frac{3}{2}R{T}_o$
• C. $R{T}_o$
• D. $\frac{1}{2}R{T}_o$

Answer 1

Answer: (A)

$2R{T}_o$

As given,
$\frac{P}{V}=P{V}^{-1}=constant$
Hence, polytropic exponent is $-1$
In a polytropic process,
$\Delta Q=\Delta U+W=(\frac{R}{\gamma -1}-\frac{R}{\eta -1})\Delta T$ where $\eta =-1$ is the polytropic exponent.
$\therefore \Delta Q=R(\frac{1}{\frac{5}{3}-1}-\frac{1}{-1-1})(2T_0-T_0)=2R{T}_0$