Question

The variation of pressure $P$ with volume $V$ for an ideal diatomic gas is parabolic as shown in the figure. The molar specific heat of the gas during this process is?

• A. $\frac{9R}{5}$
• B. $\frac{17R}{6}$
• C. $\frac{3R}{5}$
• D. $\frac{8R}{5}$

Answer 1

Answer: (B)

$\frac{17R}{6}$

This is an upright parabola, so the equation is P = $k{V}^2$

By Ideal gas equation,

P = $\frac{nRT}{V}$

So, $\frac{nRT}{V}$ = $k{V}^2$

nRT = $k{V}^3$

By first law,

dQ = dU + PdV

Let the heat capacity of the gas in this process be C, dQ = nC dT

for diatomic gas, $C_v$ = $\frac{5R}{2}$

C= $C_v$ = $\frac{5R}{2}$ + $C_v$ = $\frac{R}{3}$ = $C_v$ = $\frac{17R}{6}$