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An ideal gas has pressure p_(0), volumn V_(0) and temperature T_(0). It is taken 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 volumn at the end of the isothermal part of the process?

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Solution :
The process is shown in a `p-V` diagram in figure. The process starts from `A` and goes through `ABCD` <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_imagesHCV_VOL2_C24_S01_009_S01.png" width="80%">` <br> (b) Applying `pV = nRT at A and B` <br> `p_(0)V_(0)=nRT_(0)` <br> and `(2p_(0)V_(0)=n RT_(B)` <br> thus, `T_(B) = 2 T_(0)` <br> Thus is the temperatrue in the isothermal parts BC, <br> (c) As the process `BC` is isothermal `T_(C) = T_(B) = 2T_(0)` applying `pV = nRT` at A and C <br> `p_(0)V_(0)=nRT_(0)` <br> and `p_(0)V_(c)=nRT(2T_(0))` <br> or, `V_(c)=2V_(0)`.

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