A vessel of volume $0.2 m^{3}$ contains hydrogen gas at temperature $300 K$ and pressure 1 bar. The molar heat capacity of hydrogen at constant volume is $5 c a l / m o l / K .$ The heat (in kcal) required to raise the temperature to 400K is
$[R = \frac{25}{3} J {mol}^{- 1} K^{- 1}]$

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answer is 4.

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Detailed Solution

${(Δ Q)}_{γ} = n C_{V} Δ T, C_{V} = 5 c a l / m o l K Δ Τ = (400 - 300) = 100 K P V = n R T \Rightarrow n = \frac{P V}{R T} = \frac{10^{5} \times (0.2)}{8.31 \times 300} = 8 m o l {(Δ Q)}_{V} = n C_{V} Δ T = 8 \times 5 \times 100 = 4 k c a l$

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