| DIRECTIONS: Read the following passage and answer the questions that follows: |
| A monoatomic ideal gas is filled in a no conducting container. The gas can be compressed by a movable no conducting piston. The gas is compressed slowly to 12.5% of its initial volume. |
A) \[32{{B}_{i}}={{B}_{f}}\]
B) \[{{B}_{i}}={{B}_{f}}\]
C) \[{{B}_{i}}=32{{B}_{f}}\]
D) \[{{B}_{i}}=4{{B}_{f}}\]
Correct Answer: A
Solution :
Adiabatic bulk modulus \[B=-V\frac{dP}{dV}=\gamma P=\gamma \frac{nRT}{V}\] \[\therefore \] \[\frac{{{B}_{i}}}{{{B}_{r}}}=\frac{{{T}_{0}}}{{{V}_{0}}}\times \frac{V}{T}=\frac{{{T}_{0}}}{{{V}_{0}}}\times \frac{{{V}_{0}}/8}{4{{T}_{0}}}=\frac{1}{32}\]
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