Question

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?

Answer 1

(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)`