In the figure, a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulated material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monoatomic gas at 700K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400K. The heat capacities per mole of an ideal monoatomic gas are `C_V=3/2R, C_P=5/2R,` and those for an ideal diatomic gas are `C_V=5/2R, C_P=7/2R,`

Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gasses will be

Options

A. `550 K`
B. `525 K`
C. `513 K`
D. `490 K`

Answer

D

Explanation

Let final temperature of both compartments is T.
Heat given by lower compartment
`Q = nC_V Delta T = 2 xx3/2 R xx(700 -T)" ...(i)"`
Heat obtained by upper compartment
`Q = nC_p Delta T = 2 xx7/2 Rxx(T -400)" ...(ii)"`
Equating (i) and (ii)
`3(700 - T) =7(T-400)`
`2100 - 3T = "TT"-2800`
`4900 = 10T rArr T = 490 K`