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?

For an ideal gas with initial pressure and volume P_(i)"and " V_(i), r

1.	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?
Answer» `P_(f) = P_(i)` `P_(f) gt P_(i)` `P_(f) lt P_(i)` `P_(f)/V_(0) = P_(i)/V_(i) ` Solution :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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