P-T curve of a cyclic process is shown. Find out the works done by the gas in the given proces if number of moles of the gas are n.

Options

A. `nR(T_(1) + T_(3) - T_(4) + T_(2))`
B. `nR(T_(1) - T_(3) - T_(4) + T_(2))`
C. `nR(T_(1) + T_(3) + T_(4) - T_(2))`
D. `nR(T_(1) + T_(3) - T_(4) - T_(2))`

Answer

D

Explanation

Since paths `AB` and `CD` are isochoric, therefore work done during `AB` and `CD` is zero. Paths `BC` and `DA` are isobaric.
Hence , `W_(BC) = nRTDeltaT= nR(T_(3)-T_(2))`
`W_(DA) = nR(T_1-T_4)`
Total work done = `W_(BC)+W_(DA) = nR(T_(1)+T_(3)-T_(4)-T_(2))`.