JEE Main · 2024 · 01 Feb 2024 · Shift 1 · Heat & Thermodynamics

WhatsApp Email

Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is:

(A) $\frac{9}{4} R$ ✓ Correct
(B) $\frac{7}{4} R$
(C) $\frac{3}{2} R$
(D) $\frac{5}{2} R$

Answer: (A)

Solution

For a mixture of

n_{1}

moles of a monatomic gas (

C_{v_{1}} = \frac{3}{2} R

) and

n_{2}

moles of a diatomic gas (

C_{v_{2}} = \frac{5}{2} R

), the molar specific heat at constant volume of the mixture is

C_{v} = \frac{n _{1} C _{v_{1}} + n _{2} C _{v_{2}}}{n _{1} + n _{2}} = \frac{2 ( \frac{3}{2} R ) + 6 ( \frac{5}{2} R )}{2 + 6} = \frac{3 R + 15 R}{8} = \frac{9}{4} R

JEE Main · 2024 · 01 Feb 2024 · 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 →