$$4.0$$ g of a gas occupies $$22.4$$ litres at NTP. The specific heat capacity of the gas at constant volume is $$5.0JK-1$$ $$mol-1$$. If the speed of sound in this gas at NTP is $$952$$ $$ms-1$$, then the heat capacity at constant pressure $$is(Take$$ gas constant R $$=$$ $$8.3$$ $$JK-1mol-1)$$

Question

$$4.0$$ g  of a gas occupies $$22.4$$ litres at NTP. The specific heat capacity of the gas at constant volume is $$5.0JK-1$$ $$mol-1$$. If the speed of sound in this gas at NTP is $$952$$ $$ms-1$$, then the heat capacity at constant pressure $$is(Take$$ gas constant R $$=$$ $$8.3$$ $$JK-1mol-1)$$

Infinity Learn · Accepted Answer

Since $$4.0g$$ of a gas occupies $$22.4$$ litres at NTP, so the molecular mass of the gas $$isM=4.0$$ g $$mol-1As$$ the speed of the sound in the gas $$isv=$$γRTMwhere γ is the ratio of two specific heats, R is the universal gas constant and T is the temperature of the gas.∴γ$$=Mv2RT$$ Here, $$M=4.0$$ g $$mol-1=4.0$$×$$10-3$$ kg $$mol-1v=952$$ $$ms-1$$,$$R=8.3JK-1$$ $$mol-1$$ and $$T=273$$ K (at$$ $$NTP) ∴  γ$$=4.0$$×$$10-3$$ kg $$mol-1952$$ $$ms-128.3JK-1$$ $$mol-1(273$$ $$K)=1.6By$$ definition, γ$$=CpCv$$   or   $$Cp=$$γCv But γ$$=1.6$$ and $$Cv=5.0JK-1$$ $$mol-1$$∴  $$Cp=(1.6)5.0JK-1$$ $$mol-1$$                  $$=8.0JK-1$$ $$mol-1$$

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