One mole of an ideal gas is taken along the process in which `PV' = ` constant. The graph shown represents the variation of molar heat capacity of such a gas with respect to `x`. The value of `c'` and `x'c` respectively, are given by

Options

A. `(5)/(2) R, (5)/(2)`
B. `(5)/(2) R, (5)/(3)`
C. `(7)/(2) R, (7)/(2)`
D. `(5)/(2) R, (7)/(5)`

Answer

B

Explanation

b. At `x = oo, C = (3)/(2) R`
from `PV^(x)= ` constant
and `P^(1//x) V=` another constant
so at `x = oo, V =` constant
hence `C = C_(v) = (3)/(2) R`
and then `C_(P) = C_(v) + R = (5)/(2) C`
at `x = 0, P =` constant and `C = C'`
hence `C' = C_(P) = (5)/(2) R`
at `x = x', C = 0`, so the process is adiabatic, hence
`x' = (C_(P))/(C_(v)) = (5)/(3)`