Question

# $$5$$ mole of oxygen are heated at constant volume from $${10}^{o}C$$ to $${20}^{o}C$$. What will be the change in the internal energy of gas? The molar heat of oxygen at constant pressure, $${C}_{P}=7.03cal$$ $${ mol }^{ -1 }{ deg }^{ -1 }$$ and $$R=8.31J\quad { mol }^{ -1 }{ deg }^{ -1 }$$.

Solution

## $$R=8.31J\quad { mol }^{ -1 }{ deg }^{ -1 }=\cfrac{8.31}{4.18}cal$$ $${ mol }^{ -1 }{ deg }^{ -1 }$$$$=1.99cal$$ $${ mol }^{ -1 }{ deg }^{ -1 }$$We know that $${C}_{P}-{C}_{V}=R$$or $${C}_{V}={C}_{P}-R=7.03-1.99=5.04cal$$ $${ mol }^{ -1 }{ deg }^{ -1 }$$Heat absorbed by $$5$$ mole of oxygen in heating from $${10}^{o}C$$ to $${20}^{o}C$$$$=5\times {C}_{V}\times \Delta {T}=5\times 5.04\times 10=252cal$$Since, the gas is heated at constant volume, no external work is done,i.e., $$w=0$$So, change in internal energy will be equal to heat absorbed,$$\Delta U=q+w=252+0=252cal$$Physics

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