The equation of a certain gas can be written as T7/5P2/5= const. P Its specific heat at constant volume will be

T7/5P2/5=K⇒T7/5P−2/5=KTγP1−γ=K⇒1−γ=−2/5;1+2/5=γ⇒γ=7/5CV=Rγ−1=R7/5−1=5R2

The equation of a certain gas can be written as T7/5P2/5= const. P Its specific heat at constant volume will be

T7/5P2/5=K⇒T7/5P−2/5=KTγP1−γ=K⇒1−γ=−2/5;1+2/5=γ⇒γ=7/5CV=Rγ−1=R7/5−1=5R2

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The equation of a certain gas can be written as $\frac{T^{7 / 5}}{P^{2 / 5}} =$ const. P Its specific heat at constant volume will be

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$\frac{3}{2} R$

$\frac{5}{2} R$

$\frac{7}{2} R$

answer is B.

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Detailed Solution

$\begin{array}{l} \frac{T^{7 / 5}}{P^{2 / 5}} = K \Rightarrow T^{7 / 5} P^{- 2 / 5} = K \\ T^{γ} P^{1 - γ} = K \Rightarrow 1 - γ = - 2 / 5; 1 + 2 / 5 = γ \Rightarrow γ = 7 / 5 \\ C_{V} = \frac{R}{γ - 1} = \frac{R}{7 / 5 - 1} = \frac{5 R}{2} \end{array}$