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IF 2 mol of a gas at constant pressure, ...

IF 2 mol of a gas at constant pressure, requires 70 cal heat to increase its temperature from `30^@C` to `35^@C`, then find its degrees of freedom.

Text Solution

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Work done at constant pressure
`DeltaQ=pDeltaV=nR DeltaT=2times2times5[becauseDeltaT=(308-303)=5K`]
=20cal
Given that heat received , `Delta Q=nC_p Delta T=70 cal`
`thereforeC_p=70/(2times5)=7cal.mol^-1.K^-1`
`thereforeC_v=C_p-R=7-2=5cal.mol^-1.K^-1`
`therefore gamma=C_p/C_v=7/5`
Again `gamma=1+2/f`
`therefore1+2/f=7/5`
or,`2/f=7/5-1=(7-5)/5=2/5`
`therefore f=5`
`therefore` Degrees of freedom of the gas molecule is 5.
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