| DIRECTION: Read the passage given below and answer the questions that follows: |
| A diathermic piston divides adiabatic cylinder volume \[{{V}_{0}}\] into two equal parts as shown in the figure. Both parts contains ideal monoatomic gases. The initial pressure and temperature of gas in left compartment are \[{{P}_{0}}\] and v while that in right compartment are \[2{{P}_{0}}\] and \[2{{T}_{0}}\]. Initially the piston is kept fixed and the system is allowed acquire a state of thermal equilibrium. |
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| If the pin which was keeping the piston fixed is removed and the piston is allowed to slide slowly such that a state of mechanical equilibrium is achieved. The volume of left compartment when piston is in equilibrium is |
A) \[\frac{3}{4}{{V}_{0}}\]
B) \[\frac{{{V}_{0}}}{4}\]
C) \[\frac{{{V}_{0}}}{2}\]
D) \[\frac{2}{3}{{V}_{0}}\]
Correct Answer: C
Solution :
| [c] Let AV is change in volume in any compartment then |
| \[{{n}_{1}}=\frac{{{P}_{0}}{{V}_{0}}}{2R{{T}_{0}}}=\frac{{{P}_{f}}\left( \frac{{{V}_{0}}}{2}-\Delta V \right)}{R{{T}_{f}}}\] |
| and \[{{n}_{2}}=\frac{2{{P}_{0}}{{V}_{0}}}{2R{{T}_{0}}}=\frac{{{P}_{f}}\left( \frac{{{V}_{0}}}{2}+\Delta V \right)}{R{{T}_{f}}}\Rightarrow \Delta V=0\] |
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