An ideal gas has pressure `p_(0)`, volumn `V_(0)` and temperature `T_(0)`. It is taken by an isochoric process till its pressure is doubled. It is now isothermally expanded to get the original pressure. Finally , the gas is isobarically compressed to its original volume `V_(0)`.
(a) Show the process on a `p-V` diagram.
(b) What is the tempertaure in the isothermal part of the process?
(c) What is the volume at the end of the isothermal part of the process?

Explanation

(a) The process is shown in a `p - V` diagram in figure. The process starts from `A` and goes thourgh ABCA.
(b) Applying `pV = nRT` at A and B,
`p_(0)V_(0) = nRT`
and `(2p_(0))V_(0) = nRT_(B)`
Thus, `T_(B) = 2T_(0)`
This is the temperature in the isothermal part BC.
(c) As the process BC is isothermal, `T_(C)T_(B) = 2T_(0)`.
Applying `pV = nRT` at A and C,
`p_(0)V_(0) = nRT`
and `P_(0)V_(C) nR(2T_(0))`
`V_(C) 2V_(C)`