The equation of a certain gas can be written as ( T 7 / 5/ P 2 / 5)= constant. Its specific heat at constant volume will be :

Question

The equation of a certain gas can be written as ( T 7 / 5/ P 2 / 5)= constant. Its specific heat at constant volume will be : (A) (3/2) R (B) (5/2) R (C) (7/2) R (D) 2 R

Tardigrade Admin · Accepted Answer

The equation of a certain gas can be written as

\frac{T ^{7/5}}{P ^{2/5}} =

const

P^{- 2/5} \cdot T^{7/5} =

const

P . T^{(\frac{7/5}{- 2/5})} =

const

P T^{- 7/2} =

const.

\dots

(1)
Equation for any polytropic process,

P T^{(γ / γ - 1)} =

const..... (2)
Compare equation (1) and equation (2), we get,

\frac{γ}{γ - 1} = - \frac{7}{2}

2 γ = - 7 γ + 7

5 γ = 7

γ = \frac{7}{5}

The specific heat at constant volume will be given by

C_{V} = \frac{R}{γ - 1}

C_{V} = \frac{5 R}{2}

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

$\frac{3}{2} R$

$\frac{5}{2} R$

$\frac{7}{2} R$

2 R

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

23​R

25​R

27​R

2 R

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

$\frac{3}{2} R$

$\frac{5}{2} R$

$\frac{7}{2} R$