JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Heat & Thermodynamics

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A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by

2 0^{\circ} C

is: [Given that

R = 8.31 J mol^{- 1} K^{- 1}

]

(A)350 J
(B)700 J
(C)748 J✓ Correct
(D)374 J

Answer: (C)

Solution

At constant volume every joule we supply goes into internal energy, so

Δ Q = n C_{V} Δ T

. Helium is monatomic, which fixes

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

. For the number of moles, remember that one mole fills

22.4

L at STP, so

n = \frac{67.2}{22.4} = 3

mol. Substituting,

Δ Q = 3 \times \frac{3}{2} \times 8.31 \times 20 \approx 748

JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Single correct option

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