0.08 kg air is heated at constant volume through $5^{\circ} \mathrm{C}$. The specific heat of air at constant volume is $0.17 \mathrm{kcal} / \mathrm{kg}^{\circ} \mathrm{C}$ and $\mathrm{J}=4.18$ joule $/\mathrm{cal}$. The change in its internal energy is approximately.

JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Heat & Thermodynamics

0.08 kg air is heated at constant volume through

5^{\circ} C

. The specific heat of air at constant volume is

0.17 kcal / kg^{\circ} C

and

J = 4.18

joule

/ cal

. The change in its internal energy is approximately.

(A)318 J
(B)298 J
(C)284 J✓ Correct
(D)142 J

Answer: (C)

Solution

At constant volume,

W = 0

, so

Q = Δ U = m s Δ T

. Converting

s = 0.17

kcal/kg°C to SI using

J = 4.18

J/cal:

s = 0.17 \times 1000 \times 4.18 = 710.6 J/kg°C

Δ U = 0.08 \times 710.6 \times 5 \approx 284 J

JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Single correct option

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