The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from $0^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ when no work is done is ______. ($R$ is the universal gas constant)

JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Heat & Thermodynamics

The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from

0^{\circ} C

5 0^{\circ} C

when no work is done is ______. (

R

is the universal gas constant)

(A)175 R
(B)750 R
(C)250 R
(D)500 R✓ Correct

Answer: (D)

Solution

No work is done, so the gas is heated at constant volume and

Q = n C_{V} Δ T

. A rigid diatomic molecule has three translational and two rotational degrees of freedom and no vibrational contribution, so

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

. With

n = 4

and a rise of

50

Q = 4 \times \frac{5}{2} R \times 50 = 500 R

The heat needed is

500 R

JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Single correct option

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