A container of volume `1m^3` is divided into two equal parts by a partition. One part has an ideal gas at 300K and the other part is vacuum. The whole system is thermally isolated from the surroundings. When the partition is removed, the gas expands to occupy the whole volume. Its temperature will now be .......

Options

A. 600 K
B. 150 K
C. 300 K
D. 450 K

Answer

C

Explanation

From the first law of thermodynamics,
dQ = dU + dW
The system is thermally insulated. `" "thereforedQ=0`
The other part is vacuum. Hence the work done by the gas is expanding in that part is also zero i.e. dW = 0
[dW = PdV = 0 `" "thereforeP=0`]
`thereforedU=0`
`therefore` There is no change in internal energy and since the temperature is decided by the internal energy, there is no change in temperature.
`therefore` Final temperature = 300 K