A sound wave passing volume `1 m^(3)` is divided into two equal compartments by a partition. One of these compartments contains an ideal gas at `300 K`. The other compartment is vacuum. The whole system is thermally isolated from its surroundings. The partition is removed and the gas expands to occupy the whole volume of the container. Its temperature now would be

Options

A. `8.97 xx 10^(-4) K`
B. `8.97 xx 10^(-6) K`
C. `8.97 xx 10^(-8) K`
D. none of these

Answer

C

Explanation

c. Differentiating
`gamma T^(gamma - 1) dT P^(1 - gamma) + T^(gamma) (1 - gamma) P^(-gamma) dP = 0`
or `dT = ((gamma - 1) T)/(gamma P) = dP`
or, `dT = ((1.5 - 1)/(1.5)) ((273)/(76 xx 13.6 xx 981) xx 0.001)`
`= 8.97 xx 10^(-8) K`