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5 mole of oxygen are heated at constant volume from 10^{\circ} \mathrm{C} to 20^{\circ} \mathrm{C} . What will be the change in the internal energy of gas? The molar heat of oxygen at constant pressure, \mathrm{C}_{\mathrm{p}}=7.03 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{deg}^{-1} and \mathrm{R}=8.31 \mathrm{~J} \quad mol ^{-1} \mathrm{deg}^{-1}
Physics | Previous Year Question Papers
5 mole of oxygen are heated at constant volume from 10^{\circ} \mathrm{C} to 20^{\circ} \mathrm{C} . What will be the change in the internal energy of gas? The molar heat of oxygen at constant pressure, \mathrm{C}_{\mathrm{p}}=7.03 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{deg}^{-1} and \mathrm{R}=8.31 \mathrm{~J} \quad mol ^{-1} \mathrm{deg}^{-1}

\mathrm{R}=8.31 \mathrm{~J} \quad \mathrm{~mol}^{-1} \mathrm{deg}^{-1}=\frac{8.31}{4.18} \mathrm{cal} \mathrm{mol}^{-1} \mathrm{deg}^{-1} =1.99 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{deg}^{-1}
We know that \mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}

    \[\text { or } \mathrm{Cv}=\mathrm{Cp}-\mathrm{R}=7.03-1.99=5.04 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{deg}^{-1}\]

Heat absorbed by 5 mole of oxygen in heating from 10^{\circ} \mathrm{C} to 20^{\circ} \mathrm{C}

    \[=5 \times \mathrm{C}_{\mathrm{V}} \times \Delta \mathrm{T}=5 \times 5.04 \times 10=252 \mathrm{cal}\]

Since, the gas is heated at constant volume, no extemal work is done, i.e. _{n} \mathrm{w}=0
So, change in internal energy will be equal to heat absorbed,

    \[\Delta \mathrm{U}=\mathrm{q}+\mathrm{w}=252+0=252 \mathrm{cal}\]

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