Three moles of an ideal gas `(C_p=7/2R)` at pressure, `P_A` and temperature `T_A` is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original volume. Finally gas is compressed at constant volume to its original pressure `P_A`.
(a) Sketch P-V and P-T diagrams for the complete process.
(b) Calculate the net work done by the gas, and net heat supplied to the gas during the complete process.

Answer

(i) `(##ALN_PHY_C07(I)_E01_273_A01##) (ii) work done `(ABCA)` = `0.58RT_(A)`,heat supplied (ABCA) = `0.58RT_(A)`

Explanation

(iii) Work done by gas `W_(AB) = nR(T_(A)) ln (V_(B))/(V_(A)) = 3RT_(A)ln2`
`W_(BC) = (P_(0))/(2)(V_(0)- 2V_(0)) = -(P_(0)V_(0))/(2) = (-nRT_(A))/(2) = -(3)/(2)RT_(A)`
`W_(CA)= 0`
`therefore W_(ABCA) = RT_(A) ( 3xx0.693 -15) = 0.58RT_(A)`
`therefore DeltaQ_(ABCA) = W_(ABCA) = 0.58RT_(A)`