Question

The bulk modulus of a gas is defined as B = -VdP/dV. For an adiabatic process the variation of B is proportional to $P^n$ . For an ideal gas, n is

• A. Zero
• B. 1
• C. 5/3
• D. 2

Answer 1

The correct option is B 1

For an Ideal gas, adiabatic process follows the law $P{V}^{\gamma }=const$

i.e., $P=\frac{k}{V^{\gamma }}\Rightarrow \frac{dP}{dV}=-k\gamma V^{-\gamma -1}$

Thus, $B=-V\frac{dP}{dV}=k\gamma V^{-\gamma }=k\gamma \frac{P}{k}=\gamma P$

Thus, $B\propto P$ i.e., $n=1$