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A gass of given mass at a pressure of 10...

A gass of given mass at a pressure of `10^(5)Nm^(-2)` expands isothermally until its volume is doubled and then adiabatically until volume is again double. Find the final pressure of the gas. `(gamma=1.4)`

A

`0.76 : 1`

B

`1 : 1`

C

`0.66 : 1`

D

`0.86 : 1`

Text Solution

Verified by Experts

The correct Answer is:
a
Let V be the original volume of the gas.
For an isothermal process, PV = constant
` :. P_(i)V_(i) = P_(f)V_(f)`
` V_(f) = V_(i) (P_(i)/P_(f)) rArr V_(f) = V (P_(i)/(2P_(i))) = V/2`
For an adiabatic process, `PV^(gamma)` = constant
According to eqestin
` :. (2P_(i)) (V/2)^(gamma) = P_(f)V^(gamma)`
`rArr P_(f)/P_(i) = 2(2)^(- gamma) = 2 (2)^(-1.4) = 2 (0.38) = (0.76)/1`
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