Question

The initial pressure and volume of a gas is 'P' and 'V' respectively. First by isothermal process gas is expanded to volume '9V' and then by adiabatic process its volume is compressed to 'V' then its final pressure is ______. (Ratio of specific heat at constant pressure to constant volume = `3/2`).

Options

• 6 P

• 27 P

• 3 P

• 9 P

Answer 1

The initial pressure and volume of a gas is 'P' and 'V' respectively. First by isothermal process gas is expanded to volume '9V' and then by adiabatic process its volume is compressed to 'V' then its final pressure is 3 P.

Explanation:

`"C"_"p"/"C"_"v" = 3/2`

Case I: Isothermal process

P₁V₁ = P₂V₂

PV = P₂ × 9V

`therefore "P"_2 = "P"/9`

Case II: Adiabatic process

`"P"_2"V"_2^gamma = "P"_3"V"_3^gamma`

`"P"/9 ("9V")^gamma = "P"_3("V")^gamma`

`"P"_3 = "P"/9 9^gamma "V"^gamma/"V"^gamma = "P"/9 9^3//2 = "P"/9 xx 27` = 3P