Question

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

A
32R
B
52R
C
72R
D
2R

Solution

## The correct option is B $$\dfrac {5}{2}R$$The equation of a certain gas can be written as$$\dfrac{T^{7/5}}{P^{2/5}}=const$$$$P^{-2/5}.T^{7/5}=const$$$$P.T^{(\dfrac{7/5}{-2/5})}=const$$$$PT^{-7/2}=const$$. . . . . .(1)Equation for any polytropic process,$$PT^{(\gamma/\gamma-1)}=const$$. . . . .(2)Compare equation (1) and equation (2), we get, $$\dfrac{\gamma}{\gamma-1}=-\dfrac{7}{2}$$$$2\gamma=-7\gamma +7$$$$5\gamma=7$$$$\gamma=\dfrac{7}{5}$$The specific heat at constant volume will be given by$$C_V=\dfrac{R}{\gamma-1}$$$$C_V=\dfrac{5R}{2}$$The correct option is B.Physics

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