First slide

Heat given

Question

A cylinder of fixed capacity (of 44.8 L) contains 2 mol of helium gas at STP. What is the amount of
heat needed to raise the temperature of the gas in the cylinder by 20°C? (Take, R = 8.31J mol^-1K^-1)

Moderate

A

996 J
B

831 J
C

499 J
D

374 J

Solution

Since, the volume of cylinder is fixed and helium is a monoatomic gas.
The internal energy = $μ C_{V} Δ T$
$\Rightarrow U = \frac{1}{2} f μ R Δ T (∵ C_{V} = \frac{1}{2} f R)$
$U = \frac{1}{2} \times 3 \times 2 \times 8.31 \times 20$ $(∵ f = 3)$
$= 498.6 \approx 499 J$

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