Question

An ideal gas whose adiabatic exponent is $\gamma$ is expanded so that the amount of heat transferred to the gas is equal to the decrease of its internal energy$.$ Molar heat capacity of the gas for this process is

• A. $\frac{R}{1-\gamma }$
• B. $\frac{R}{\gamma -1}$
• C. $R$
• D. $\frac{R}{2}$

Answer 1

Answer: (B)

$\frac{R}{\gamma -1}$

Since, the heat exchnage is equal to chnage in its interal energy.

i.e.,

Work done =0

i.e. $dv=n{C}_{v}dt$

$\left(\frac{dv}{ndT}\right)=C_v$

So, molar heat capacity will be $C_v$

Now, we know that

$C_P-C_v=R$....(1)

and $\frac{C_p}{C_v}=\gamma$

$\Rightarrow C_p=\gamma C_v$

Putting m (i)

$\gamma C_v-C_v=R$

$\Rightarrow C_v=\frac{R}{\gamma -1}$