InterviewSolution
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InterviewSolution
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Find the molar heat capacity of an ideak gas in a polytropic process `p V^n = const` if the adiabatic exponent of the gas is equal to `gamma`. At what values of the polytropic constant `n` will the heat capacity of the gas be negative ? |
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Answer» In the polytropic process work done by the gas `A = (vR[T_i - T_f])/(n - 1)` (where `T_i` and `T_f` are initial and final temperature of the gas like in adiabatic process) and `Delta U = (vR)/(gamma - 1)(T_f - T_i)` By the first law of thermodynamics `Q = Delta U + A` =`(vR)/(gamma - 1)(T_f - T_i)+(vR)/(n -1) (T_i - T_f)` =`(T_f - T_i) vR[(1)/(gamma - 1) -(1)/(n -1)] = (vR[n - gamma])/((n - 1)(gamma -1)) Delta T` According to definition of molar heat capacity when number of moles `v = 1` and `Delta T = 1` then `Q` = Molar heat capacity. Here, `C_n = (R(n - gamma))/((n - 1)(gamma - 1)) lt 0 "for" 1 lt n lt gamma`. |
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