5 moles of unknown gas is heated at constant volume from $10^{\circ}\mathrm{C}$ to $20^{\circ}\mathrm{C}$. The molar specific heat of this gas at constant pressure $\mathrm{c}_{\mathrm{p}}=8\mathrm{~cal}/\mathrm{mol}.^{\circ}\mathrm{C}$ and $\mathrm{R}=8.36\mathrm{~J}/\mathrm{mol}.^{\circ}\mathrm{C}$. The change in the internal energy of the gas is ______ calorie.

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Heat & Thermodynamics

5 moles of unknown gas is heated at constant volume from

1 0^{\circ} C

2 0^{\circ} C

. The molar specific heat of this gas at constant pressure

c_{p} = 8 cal / mol .^{\circ} C

and

R = 8.36 J / mol .^{\circ} C

. The change in the internal energy of the gas is ______ calorie.

Answer: 300

Solution

At constant volume the change in internal energy is

Δ U = n C_{V} Δ T

. Mayer's relation gives

C_{V} = C_{P} - R

; converting

R = 8.36 J/mol \cdot^{\circ} C = 2 cal/mol \cdot^{\circ} C

, so

C_{V} = 8 - 2 = 6 cal/mol \cdot^{\circ} C

. With

n = 5

and

Δ T = 20 - 10 = 1 0^{\circ} C

Δ U = 5 \times 6 \times 10 = 300 cal

. The internal energy of the gas increases by

300

calories.

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Integer answer

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