First slide

Heat ;work and internal energy

Question

A container closed by a freely moving piston contains a mixture of hydrogen and helium gases of total mass 12 gm. A heat of 150 kJ is transferred to the gas at constant pressure and in this process gas performs 50 kJ work. Find mass of hydrogen (in gm) in the mixture.

Moderate

Solution

$\begin{array}{l} {nC}_{P} ΔT = 150 \\ nRΔT = 50 \end{array}$
$\Rightarrow n C_{P} △ T = 3 n R △ T$
$\begin{array}{l} \Rightarrow n_{1} C_{P_{1}} + n_{2} C_{P_{2}} = 3 (n_{1} + n_{2}) R \\ \Rightarrow n_{1} (\frac{5 R}{2}) + n_{2} (\frac{7 R}{2}) = (3) (n_{1} + n_{2}) R \\ \Rightarrow 5 n_{1} + 7 n_{2} = 6 n_{1} + 6 n_{2} \\ \Rightarrow n_{1} = n_{2} \\ A l s o, n_{1} (4) + n_{2} (2) = 12 \\ n_{1} = n_{2} = 2 \end{array}$
Mass of hydrogen = 4 gm

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