An ideal gas is taken from the state A (pressure p, volume V) to the state B (pressure `p/2`, volume 2V) along a straight line path in the p-V diagram. Select the correct statement(s) from the following.

Options

A. The work done by the gas in process `AB` is greater than the work that would be done if the system were taken from `A` to `B` along the isotherm
B. In the `P-T` diagram, the path `AB` becomes a part of parabola
C. In the `P - T` diagram, the path `AB` becomes a part of hyperbola
D. In going from `A` to `B`, the temperature `T` of the gas first increase to a maximum value and then decreases

Answer

A, B, D

Explanation

`i.` Work done `=` area under the curve,
`W_(1)=(P+(P)/(2))(2V-V)=(3)/(2) PV`
Work done under isothermal process,
`W_(2)=RTxx2.3026 log((2V)/(V))`
`=0.693 RT=0.693 PV`
`:. W_(1)gt W_(2), i.e., ` option `(a)` is correct.
`(ii)` Let `P_(0)` and `V_(0)` be the intercept on the `P` and `V` axes.
Now the equation of straight line would be
`P=(P_(0))/(V_(0))xxV+P_(0)`
`( :' y = mx + c)`
Further `PV=RT` or `P=(RT)/(V)`
`(` This represents parabola, so option `(b)` is also correct. `)`