Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be [2014]

Question

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 monatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas are $C_{V} = \frac{3}{2} R, C_{P} = \frac{5}{2} R$ and those for an ideal diatomic gas are $C_{V} = \frac{5}{2} R, C_{P} = \frac{7}{2} R .$

Q. Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be [2014]

Smart Achievers · Accepted Answer

(4)

$Let T be the final temperature of the gases when equilibrium is achieved.$

$Heat lost by monoatomic gas at constant volume$ $= Heat gained by diatomic gas at constant pressure$

$∴$ $n C_{v 1} (700 - T) = n C_{p 2} (T - 400)$

$\frac{3}{2} R (700 - T) = \frac{7}{2} R (T - 400)$

$\Rightarrow 2100 - 3 T = 7 T - 2800$

$\Rightarrow 10 T = 4900$

$∴$ $T = 490 K$

Solution

1 550 K

2 525 K

3 513 K

4 490 K

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