Discussion Forum

1)

In the figure a container is shown to have a movable (without friction) position on top. The container and the piston are all made of perfectly insulating 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   $C_{v}=\frac{3}{2}R,C_{p}=\frac{5}{2}R,$  , and those for an ideal diatomic  gas are  $C_{v}=\frac{5}{2}R,C_{p}=\frac{7}{2}R,$

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

Answer:

Option D

Explanation:

 Let final equilibrium temperature of gases is T 

 Heat rejected by gas by lower cmpartment

          $=nC_{v}\triangle T$

  $=2\times \frac{3}{2}R(700-T)$

  Heat  received by the gas in above compartment

  =  $=nC_{p}\triangle T$

      $=2\times \frac{7}{2}R(T-400)$

 Equating the two , we get

   2100-3T= 7T-2800

 $\Rightarrow$            $ T=490 K$