For two different gases X and Y , having degrees of freedom f₁ and f₂ and molar heat capacities

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11.Thermodynamics

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For two different gases $X$ and $Y$, having degrees of freedom $f_1$ and $f_2$ and molar heat capacities at constant volume $C_{V1}$ and $C_{V2}$ 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

Both $(B)$ and $(C)$

Solution

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 $\mathrm{B}, \mathrm{C}$

Standard 11

Physics

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