1.

An ideal gas is expanding such that `PT^2=constant.` The coefficient of volume expansion of the gas is-A. `1/T`B. `2/T`C. `3/T`D. `4/T`

Answer» Correct Answer - C
`pT^(2)=`constant
`((nRT)/(V))T^(2)=`constant
`T^(3)V^(1)=`constant
Differentiating the equation, we get
`(3T^(3))/(V)dT-(T^(3))/(V(3))dV=0`
`3dT=(T)/(V)dV`
From the equation, `dV=VgammadT`
`gamma=` coefficient of volume expansion of gas `=dV//VdT` .
From Eq. (i) , `gamma=(dV)/(VdT)=(3)/(T)`


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