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

When a ideal gas with pressure P and volume V is compressed isothermal

1.	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
Answer» `(1)/(2)` `(1)/(2^(1.5))` 2 `2^(1.5)` Solution :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)`