We have the following experimental setup:
Before the experiment starts: $$p_1=p_2; \space V_1=V_2; T_1=T_2+\Delta T$$
The experiment starts and both the containers are heated so that the temperature difference $\Delta T$ remains constant (Edit: I wanted this to mean that there is no physical deformation, expansion or contraction of the containers. The piston is still allowed to move). The Volume of the containers also stays constant. Does the piston move to the left or to the right?
We have been discussing this question for an hour in our study group and we haven't really come to a conclusion. There are basically two hypothesis:
- Since the piston didn't move before the containers were heated, the piston won't move after the containers are heated because the tempereature will be increased by the same amount in both containers.
- Applying the ideal gas law $$pV=Nk_bT$$ and taking into consideration the fact that before the experiment started, both the containers had the same volume ($V_1=V_2$)and pressure ($p_1=p_2$) but different temperatures, it follows that there must be more particles/molecules in container 2 to "compensate" the higher temperature in the first one. Heating both containers by the same amount (equal temperature increase) implies more energy supplied to container 2 which will cause the piston to move left.
Can you give us a hint if we are going in the right direction with any of these hypothesis?