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For an ideal gas with initial pressure a...

For an ideal gas with initial pressure and volume `P_(i)" and " V_(i)`, respectively, a reversible isothermal expansion happers, when its volume becomes `V_(0)`. Then it is compressed to its original volume `V_(i)`by a reversible adiabatic process. If the final pressure is `P_(f)`, then which of the following statement is true?

A

`P_(f) = P_(i)`

B

`P_(f) gt P_(i)`

C

`P_(f) lt P_(i)`

D

`P_(f)/V_(0) = P_(i)/V_(i) `

Text Solution

Verified by Experts

The correct Answer is:
b
For isothermal expansion , `P_(i) V_(i) = P_(0)V_(0)` ….(i)
`P_(0)` is the pressure of the gas corresponding to volume `V_(0) `.
For adiabatic compression , `P_(0) V_(0)^(gamma) = P_(f)V_(i)^(gamma)` …..(ii)
or , `(P_(i)V_(gamma))/V_(0)xx V_(0)^(gamma) = P_(f) V_(i)^(gamma) " or , " P_(i)/P_(f) = (V_(i)/V_(0))^(gamma -1) `
Since , `V_(i) lt V_(0) " so " P_(f) gt P_(i) `
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