Question

During an adiabatic process, the pressure of a gas is proportional to the to the cube of its temperature. The ratio of $\frac{C_p}{C_v}$ for the gas is:

• A. $3/5$
• B. $4/3$
• C. $5/3$
• D. $3/2$

Answer 1

Answer: (D)

$3/2$

$\text{Given:-}$ (i) Adiabatic process

(ii)The pressure of a gas is found to be proportional to the cube of its

absolute temperature.

$\text{Solution:-}$ In an Adiabatic process

$\Rightarrow P\propto T^{\frac{\gamma }{\gamma -1}}\propto T^3$

$\therefore \frac{\gamma }{\gamma -1}=3$

$\Rightarrow 3\gamma -3=\gamma$

$\Rightarrow 2\gamma =3$

$\gamma =\frac{3}{2}$

We know that,

$\gamma =\frac{C_P}{c_V}$

So,

$\frac{C_P}{c_V}=\frac{3}{2}$

$\text{Hence the correct option is D}$