JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Heat & Thermodynamics

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A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by

20. 0^{\circ} C

will be:
(Given gas constant

R = 8.3 JK^{- 1} mol^{- 1}

)

(A)249 J
(B)415 J
(C)498 J✓ Correct
(D)830 J

Answer: (C)

Solution

At STP, 22.4 L contains 1 mole of gas. So 44.8 L contains

n = \frac{44.8}{22.4} = 2

moles. For helium (monatomic),

C_{v} = \frac{3}{2} R

. The heat required at constant volume is

Δ Q = n C_{v} Δ T = 2 \times \frac{3}{2} R \times 20 = 60 R = 60 \times 8.3 = 498

JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Single correct option

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