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.

Answer

`(1)/(2)R(T_2)-T_(1))`

Explanation

`PV^(k) = constatn`
`V rarr alpha v` `(alpha =4)`
`P rarr P//beta (beta =8)`
`V^(k) = (P//beta)(dv)^(k)`
`beta = (alpha)^(k)`
Taking log
`(lnbeta)/(lnalpha) =k`
`C= CV+(Pdv)/(ndT)`
`C=(3R)/(2)+(P_(f)V_(f)-P_(i)V_(i))/((1-k)ndT)`
`C=(3R)/(2) + (nRdT)/(ndT)`
`C= (3R)/(2) +(nRdT)/((1-k)ndT)`
`k = 3//2` rArr `C=(3R)/(2)-R//2 =R`