Two moles a monatomic gas in state `A` having critical pressure `P_(0)` and temperature `3 T_(0)` is taken to a state `B` having pressure `3 P_(0)` and temperature `T_(0)//3` by the process of equation `P^(2) T` = constant. Then state `B` is taken to state `C` keeping the volume constant and it comes back to initial state `A` keeping temperature constant.
a. Plot a `P` and `T` graph. (P on the y-axis and `T` on the x-axis).
Find the net work done and heat supplied to the gas during the complete cycle.

Explanation

Work done in process `AB`
`Delta W_(AB) = (2 r [(T_(0))/(3) - 3 T_(0)])/(((1)/(3) - 1))`
`W = - 8 RT_(0)`
`Delta Q_(AB) = du + Delta w = - nC_(v) Delta T - 8 RT_(0)`
`Delta Q_(AB) = - 16 RT_(0)`
For process `B rarr C, W_(BC) = 0`
`du = 8 RT_(0), Delta Q_(BC) = 8 RT_(0)`
and `C rarr A` (isothermal process)
`Delta W_(CA) = 2 R (3 T_(0)) 1n (V_(f))/(V_(i)) ((V_(f))/(V_(i)) = 27)`
`Delta W_(CA) = 18 RT_(0) 1n 3`
`Delta Q_(CA) = 18 RT_(0) 1n 3`
Net work done,
`Delta W = Delta W_(AB) + Delta W_(BC) + Delta W_(CA)`
`= - 8 RT_(0) + 0 + 18 RT_(0) 1n 3`
`Delta W = RT_(0) + (18 1n 3 - 8)`
`Delta Q_(n e t) = Delta Q_(BC) + Delta Q_(CA)`
`= - 8 RT_(0) + 18 RT_(0) 1n 3`
`Delta Q_(n e t) = RT_(0) (18 1n 3 + 8)`