JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Heat & Thermodynamics

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

(A) $\frac{P}{2}$
(B)3P✓ Correct
(C)2P
(D)P

Answer: (B)

Solution

The bulk modulus is defined as

B = - V \frac{d P}{d V}

.

Given

P = a V^{- 3}

, differentiating with respect to V:

\frac{d P}{d V} = - 3 a V^{- 4} = - 3 a \cdot \frac{1}{V ^{4}}

Since

P = a V^{- 3}

, we have

a = P V^{3}

. Substituting:

\frac{d P}{d V} = - 3 \cdot \frac{P V ^{3}}{V ^{4}} = - \frac{3 P}{V}

Therefore:

B = - V \cdot (- \frac{3 P}{V}) = 3 P

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Heat & Thermodynamics →

More JEE Main questions on Heat & Thermodynamics

A cylindrical tube $A B$ of length $l$ , closed at both ends contains an ideal gas of 1 mol having molecular weight $M$ . The tube is rotated in a horizontal plane with constant angular velocity $ω$ about an axis perpendicular to $A B$ and passing through the edge at end A, as s …
JEE Main 2026View solution →
Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $10 0^{\circ} C$ and $4 0^{\circ} C$ respectively. Given the thermal conductivity of rod x is three …
JEE Main 2026View solution →
The volume of an ideal gas increases 8 times and temperature becomes $(1/4)^{th}$ of initial temperature during a reversible change. If there is no exchange of heat in this process ( $Δ Q = 0$ ) then identify the gas from the following options (Assuming …
JEE Main 2026View solution →
Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is …
JEE Main 2026View solution →
An insulated cylinder of volume $60 cm^{3}$ is filled with a gas at $2 7^{\circ} C$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 cm^{3}$ while allowing the temperature to rise to $7 7^{\circ} C$ . The fin …
JEE Main 2026View solution →
The r.m.s speed of oxygen molecules at $4 7^{\circ} C$ is equal to that of the hydrogen molecules kept at $____$ $^{\circ} C$ . (Mass of oxygen molecule/mass of hydrogen molecule=32/2)
JEE Main 2026View solution →