JEE Advanced · 2012 · 08 Apr 2012 · Paper 2 · Heat & Thermodynamics

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Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35°C. The amount of heat required in raising the temperature is nearly (take

R = 8.31 J / mol . K

)

(A)62 J
(B)104 J
(C)124 J
(D)208 J✓ Correct

Answer: (D)

Solution

Since the balloon is fully expandable with no energy required for expansion, the process is isobaric (constant pressure). For an isobaric process,

Δ Q = n C_{p} Δ T

. For helium (monatomic gas),

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

. Therefore,

Δ Q = 2 \times \frac{5}{2} \times 8.31 \times (35 - 30) = 5 \times 8.31 \times 5 = 207.75 \approx 208

JEE Advanced · 2012 · 08 Apr 2012 · Paper 2 · Single correct option

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