When a ideal gas with pressure P and volume V is compressed isothermally to one fourth of its volume, the pressure is `P_(1)`. When the same gas is compressed polytropically according to the equation `PV^(1.5)` = constant to one fourth of its initial volume, the pressure is `P_(2)`. THe ratio `(P_(1))/(P_(2))` is

Options

A. `(1)/(2)`
B. `(1)/(2^(1.5))`
C. 2
D. `2^(1.5)`

Answer

A

Explanation

For a isothermal process, PV = constant
`:. PV = P_(1) (V)/(4)` or `P_(1) = 4P`
For the polytropic process, `PV^(1.5)` = constant
`:. PV^(1.5) = P_(2)((V)/(4))^(1.5)` or `P_(2) = (2^(2))^(3//2)P = 8P :. (P_(1))/(P_(2)) = (1)/(2)`