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Internal Energy

A cylinder of...

Question

A cylinder of ﬁxed capacity (of 44.8L) contains 2 moles of He gas at STP. What is the amount of heat needed to raise the temperature of the gas in the cylinder by $20^{\circ} C$ ? [R = 8.31 J/molK]

A

996J

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B

831J

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C

499J

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D

374J

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Solution

The correct option is C 499J
Cylinder is of fixed capacity (volume constant)
$Q = n C_{v} Δ T$
if volume constant $Q = n C_{V} Δ T$ if pressure $Q = n C_{P} Δ T$ constant
$n = 2 m o l, C_{v} (H e g a s) = \frac{3}{2} R, Δ T = 20 K$
$Q = 2 \times \frac{3}{2} \times 8.31 \times 20$
$= 498.6 J = 499 J$

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