Question

A gas undergoes a change according to the law $P = P_{0}e^{\alpha V}$. The bulk modulus of the gas is

• A. P
• B. αPV
• C. αP
• D. $\frac{PV}{\alpha}$

Answer 1

Answer: (B)

αPV

Answer 2

$P = P_{o}e^{\alpha V}$⇒ $\frac{dP}{dV} = P_{o}e^{\alpha V}\alpha = P\alpha$

[As $P = P_{o}e^{\alpha V}$]

$\frac{dP}{dV}V = P\alpha V$ ⇒ $\frac{dP}{(dV/V)} = P\alpha V$ $\therefore K = P\alpha V$