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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 happens, 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

We know, slope of adiabatic curve > slope of isothermal curve.
When the gas of volume `V_(0)` is compressed adiabatically to its initial volume `V_(i)`, the slope of the curve will be greater than isothermal curve. Here final pressure `p_(f)` at initial volume `V_(i)` will be greater that `P_(i)`.
`:. P_(f) > P_(i)`.
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