The correct relation between $\gamma=\frac{C_p}{C_v}$ and temperature T is :

(A) $\gamma \propto \frac{1}{\sqrt{T}}$

(C) $\gamma \propto \frac{1}{T}$

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Heat & Thermodynamics

The correct relation between

γ = \frac{C _{p}}{C _{v}}

and temperature T is :

(A) $γ \propto \frac{1}{T}$
(B) $γ \propto T^{0}$ ✓ Correct
(C) $γ \propto \frac{1}{T}$
(D) $γ \propto T$

Answer: (B)

Solution

The ratio

γ = \frac{C _{p}}{C _{v}}

is fixed by the number of degrees of freedom of the molecules, which depends on whether the gas is monatomic, diatomic or polyatomic, and not on how hot the gas is. For an ideal gas it therefore keeps the same value at every temperature, so

γ \propto T^{0}

JEE Main · 2023 · 31 Jan 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 →