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An ideal gas is taken from the state A (...

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 from the following

A

In PT diagram path AB becomes a part of hyperbola.

B

Work done by the gas In the process A to B is more than the work done if the system were taken from A to B along an isotherm.

C

In `TV` diagram,t he path `AB` becomes a part of parabola.

D

in going from A to B the temperature T of the gas first increases to a maximum value and then decreases.

Text Solution

Verified by Experts

The correct Answer is:
A, B, D

Area under PV curve is work done.
Area under AB straight line is greater than area under isotherm therefore `W_("process")gtW_("isotherm")`
let `P=alphaV+beta` (from equation of straight line AB)
`PV-alphaV^(2)+betaV=nRT`
`impliesT=(1)/(nR)(-alphaV^(2)+betaV)` equation of parabola
`(d^(2)T)/(dV^(2))=-2alpha=-ve`
`TpropPV`
`(PV_(A)=(P.V)BimpliesT_(A)=T_(B)`
since `T_(A)=T_(B)` increases b/w A and B reaches a maximum and again decreases to reach the same temperature.
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