Question

One mole of argon is expanded polytropically $(\eta =1.5)$ and its temperature falls by $26K$. Find the heat gained by gas lf $R=8.4J/mol-K$.

• A. $109.2J$
• B. $200.3J$
• C. $60J$
• D. $90J$

Answer 1

Answer: (A)

$109.2J$

In a polytropic process heat absorbed:
$Q=C_v\Delta T+{\int }_{V_1}^{V_2}PdV=\frac{R}{\gamma -1}\Delta T+\frac{P_2{V}_2-P_1{V}_1}{\eta -1}=\frac{R}{\gamma -1}\Delta T+\frac{R\Delta T}{1-\eta }....\left(1\right)$
where $\eta$ is the polytropic coefficient

For Argon: $\gamma =\frac{2+f}{f}=\frac{2+3}{3}=\frac{5}{3}$ where $f$ is the no. of degrees of freedom

Given $\eta =1.5$
$\Delta T=-26$ since temp decreases

Substituting the values in eqn(1) we get,
$\Delta Q=\frac{8.4}{\frac{5}{3}-1}(-26)+\frac{8.4}{1-1.5}\times (-26)=(8.4\times 26)(-\frac{3}{2}+2)=109.2J$