An ideal gas has an adiabatic exponent `gamma`. In some process its molar heat capacity varies as `C = alpha//T`,where `alpha` is a constant Find : (a) the work performed by one mole of the gas during its heating from the temperature `T_0` to the temperature `eta` times higher , (b) the equation of the process in the variables `p, V`.A. `a ln eta`B. `(1)/(aln eta)`C. `aln eta -((eta-1)/(gamma-1))RT_(0)`D. `alneta -(gamma-1)RT_(0)`

An ideal gas has an adiabatic exponent `gamma`. In some process its mo

1.	An ideal gas has an adiabatic exponent `gamma`. In some process its molar heat capacity varies as `C = alpha//T`,where `alpha` is a constant Find : (a) the work performed by one mole of the gas during its heating from the temperature `T_0` to the temperature `eta` times higher , (b) the equation of the process in the variables `p, V`.A. `a ln eta`B. `(1)/(aln eta)`C. `aln eta -((eta-1)/(gamma-1))RT_(0)`D. `alneta -(gamma-1)RT_(0)`
Answer» Correct Answer - C `dW = dQ - dU , dW = nCdT - nC_(v)dT` `W = int CdT - int C_(v)dT , = int (a)/(T)dT - C_(v) DeltaT` ` = a In ((etaT_(0))/(T_(0))) - ((T_(2)-T_(1))R)/(gamma-1)` `W = a In eta (-(eta-1)T_(0)R)/(gamma-1)`

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