Question

For two different gases X and Y, having degrees of freedom $f_1$ and $f_2$ and molar heat capacities at constant volume $C_{v_1}$ and $C_{v_2}$ respectively.The $\ln P$ versus $\ln V$ graph is plotted for adiabatic process, as shown

• A. $f_1>f_2$
• B. $f_2>f_1$
• C. $C_{v_2}>C_{v_1}$
• D. $C_{v_1}>C_{v_2}$

Answer 1

Answer: (B), (C)

$f_2>f_1$
$C_{v_2}>C_{v_1}$

Since the two equations are of the form, $\ln P+m\ln V=C$

Hence, $P{V}^m=constant$

Thus, slope of the graph is equal to $\gamma$.

$\gamma =\frac{f+2}{f}=1+\frac{2}{f}$

Since ${\gamma }_1>{\gamma }_2$, thus $f_2>f_1$

Since $C_V=\frac{f}{2}R$, thus $C_{V_2}>C_{V_1}$

Answer is B,C.