For an ideal gas $\mathrm{PT}^{3}=$ constant. Find the coefficient of volume expansion of the gas is:

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Heat & Thermodynamics

For an ideal gas

PT^{3} =

constant. Find the coefficient of volume expansion of the gas is:

(A) $1/ T$
(B) $3/ T$
(C) $2/ T$
(D) $4/ T$ ✓ Correct

Answer: (D)

Solution

For one mole

P V = R T

, and the constraint

P T^{3} = const

gives

P \propto T^{- 3}

. Substituting,

V = \frac{R T}{P} \propto \frac{T}{T ^{- 3}} = T^{4}

, so

V = c T^{4}

. The coefficient of volume expansion is

γ = \frac{1}{V} \frac{d V}{d T} = \frac{1}{c T ^{4}} (4 c T^{3}) = \frac{4}{T} .

JEE Main · 2021 · 27 Aug 2021 · 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 →