The temperature of a hypothetical gas increases to `sqrt(2)` times when compressed adiabatically to half the volume. Its equation can be written as

Options

A. `PV^(3//2)` constant
B. `PV^(5//2)` = constant
C. `PV^(7//3)`= constant
D. `PV^(4//3)` = constant

Answer

A

Explanation

For adiabatic process
`TV^(gamma-1)` = constant
`(T_1)/(T_2)=((V_2)/(V_1))^(gamma-1) implies (1/2)^(gamma-1)=1/sqrt2 implies gamma = 3/2`
`:. PV^(3//2)` = constant.