Find the relatio between volume and temperature of a gas in a process, in which the molar heat capacity C varies with temperature T as `C=C_(V)+alphaT`. [`alpha` is a constant] .
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By first law of thermodymanics, molar specific heat is given as
`C=C_(V)+R((dV//V)/(dT//T))` . . . . (i)
Compare (i) with given equation
`C+C_(V)+alphaT=C_(V)+R((dV//V)/(dT//T))`
`impliesR(dV//V)=alphaT((dT)/(T))`
`implies(dV)/(V)=(alphadT)/(R)`
`implieslog” “V=(alphaT)/(R)+logC`
`implieslogV=log_(e)e(alphaT)/(R)+logC`
`implieslog” “V=log[C.e^(alphaT//R)]`
`impliesVe^(-alphaT//R)=C`.