Question

The ratio of adiabatic bulk modulus and isothermal bulk modulus of a gas is $(\gamma =\frac{C_p}{C_v})$

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

Answer 1

The correct option is B

$\gamma$

Bulk modulus is defined as

$B=-\frac{V\Delta P}{\Delta V}$

For adiabatic process, $P{V}^{\gamma }$ = constant. Differentiating partially, we get

$\Delta P{V}^{\gamma }+P\gamma V^{\gamma -1}\Delta V=0$

or $-\frac{V\Delta P}{\Delta V}=\gamma P$

Therefore $B_a=\gamma P$

Similarly, for isothermal process, PV = constant gives

$B_i=P$

Hence $\frac{B_a}{B_i}=\gamma$