Two moles of a gas `(gamma=5//3)` are initially at temperature `27^@C` and occupy a volume of 20 times. The gas is first expanded at constant pressure until the volume is doubled. Then, it is subjected to an adiabatic change until the temperature returns to its initial value.
(a) Sketch the process on a p-V diagram.
(b) What are the final volume and pressure of the gas?
(c) What is the work done by the gas?

Answer

(i) `(##ALN_PHY_C07(I)_E01_275_A01##)` (ii) `113 L , 0.44 xx 10^(5)N//m^(2)` , (iii)`12459J`

Explanation

(ii) Process `AB` : `(V_(A))/(T_(A)) = (V_(B))/(T_(B))`
`T_(B) = (V_(B))/(V_(A)) T_(A) = 2T_(A) = 600K`
Process `BC` : `T_(B)V_(B)^(gamma-1) = T_(C)V_(C)^(gamma-1)`
`implies V_(C) = 80sqrt(2) "Litre" = 113L`
For end states A & C `(P_(A).V_(A))/(T_(A)) = (P_(C)V_(C))/(T_(C))= nR implies P_(C) = 0.44 xx 10^(5)N//m^(2)`
(iii) Work done `W_(AB) = P_(A)(2V_(0) -V_(0))= nRT_(A) = 600R, W_(BC) = (nR(T_(B) - T_(C))/(gamma-1)) = (3)/(2)nR (6000-300) = 900R`