An ideal gas at pressure P and volume V is expanded to volume 2V. Column I represents the thermodynamic process used during expansion. Column II represents the work done during processes in the random order.

Options

A. `A rarr Q, B rarr R, C rarr P`
B. `A rarr Q, B rarr P, C rarr R`
C. `A rarr P, B rarr Q, C rarr R`
D. `A rarr R, B rarr Q, C rarr P`

Answer

A

Explanation

For an isobaric process,
Work done `= Pdelta V = P(2V - V) = PV`
For an isothermal process,
Work done `= RT ln ((2V)/(V)) = PV ln 2`
For an adiabatic process, `PV^(gamma) = P_(1)(2V)^(gamma)`
or `P_(1) = ((1)/(2))^(gamma) P = P_(2)^(-gamma)`
`:.` Work done `= (PV - P_(1)(2V))/(gamma - 1) = (PV (1-2^(1-gamma)))/(gamma - 1)`
Thus, `A rarr Q, B rarr, C rarr P`