One mole of an ideal monoatomic gas undergoes a cyclic process as shown in figure . Temperature at point `1` =`300K` and process `2-3` is isothermal .

Heat capacity of process `1rarr 2` is

Options

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

Answer

D

Explanation

`C = (DeltaQ)/("n"DeltaT) = (n((3R)/(2)DeltaT) +DeltaW)/(nDeltaT) = (3R)/(2) + (4P_(0)V_(0))/("n"DeltaT) = (3R)/(2) + (P_(0)V_(0))/(n(2T_(0))) = (3R)/(2) + (R)/(2) = 2R`
`DeltaQ = n(2R)(DeltaT_(12)) + (W_(23)) = n(2R)(8T_(0)) + nR(9T_(0))ln(3) = nRT_(0) (16 +9ln3)`