Q72 / 90 · JEE Main 2023 (13 Apr Shift 1) · Physics

Under isothermal condition, the pressure of a gas is given by $P = a V^{- 3},$ where $a$ is a constant and $V$ is the volume of the gas. The bulk modulus at constant temperature is equal to

Correct answer
A
$3 P$
B
$P$
C
$2 P$
D
$\frac{P}{2}$

Solution

The data given is
$P = a V^{- 3}$
Bulk modulus is given by,
$B = - \frac{d P}{\frac{d V}{V}} = - V \frac{d P}{d V}$
$= - V \frac{d}{d V} \{\frac{a}{V^{3}}\}$
$= - V [\frac{- 3 a}{V^{4}}]$
$= \frac{3 a}{V^{3}} = 3 P$

Hence, the correct answer is option: 'A'.

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Under isothermal condition, the pressure of a gas is given by P=aV–3, where a is a constant and V is the volume of the gas. The bulk modulus at constant temperature is equal to

Solution

Relevant Questions

Under isothermal condition, the pressure of a gas is given by $P = a V^{- 3},$ where $a$ is a constant and $V$ is the volume of the gas. The bulk modulus at constant temperature is equal to