In a certain polytropic process the volume of argon was increased `alpha= 4.0` times. Simultaneously, the pressure decreased `beta = 8.0` times. Find the molar heat capacity of argon in this process. Assuming the gas to be ideal.

Explanation

Let the process be polytropic according to the law `pV^n = constant`
Thus, `p_f V_f^n = p_i V_i^n` or, `((p_i)/(p_f)) = beta`
So, `alpha^n = beta` or `1n beta = n 1n alpha` or `n = (1n beta)/(1 n alpha)`
In the polytropic process molar heat capacity is given by
`C_n (R(n - gamma))/((n - 1)(gamma - 1)) = (R)/(gamma - 1) -(R)/(n - 1)`
=`(R)/(gamma - 1) = (R 1n alpha)/(1 n beta - 1n alpha)`, where `n = (1 nbeta)/(1n alpha)`
So, `C_n = (8.314)/(1.66 0-1)-(8.314 1n 4)/(1 n 8 - 1n 4) = -42 J//mol.K`.