A cylinder of fixed capacity 44.8 litre. contains a monatomic gas at standard temperature and pressure. The amount of heat required to increse the temperature of cylinder by $10^{\circ}$ C will be. (R = universal gas constant)

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10R

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20R

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30R

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Solution

The correct option is D 30R
As we know 1 mol of any ideal gas at STP occupies a volume of 22.4 liters.
Hence number of moles of gas $μ = \frac{44.8}{22.4}$ = 2
Since the volume of cylinder is fixed,
Hence $(△ Q)_{V}$ = $μ (C_{V}) △ T = 2 \times \frac{3}{2} R \times 10$ = 30R( $∵ (C_{V})_{m o n o} = \frac{3 R}{2}$ ))

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