Question

A gas follows a process $T{V}^{n-1}$ = constant, where T = absolute temperature of the gas and V = volume of the gas. The bulk modulus of the gas in the process is given by

• A. (n - 1)P
• B. P / (n - 1)
• C. nP
• D. P / n

Answer 1

Answer: (C)

nP

The bulk modulus for a gas is given by:

$K=-V\frac{dP}{dV}$

and given that:

$T{V}^{n-1}=constant$

Ideal gas equation gives us the relation

$PV=nRT$

i.e.

$P{V}^n=constant$

Differentiating we get:

$Pn{V}^{n-1}+V^n\frac{dP}{dV}=0$

i.e.

we get

$\frac{dP}{dV}=-\frac{nP}{V}$

Hence bulk modulus $K=nP$

Hence option C is correct.