| 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) \[4{{T}_{0}}\]
B) \[3{{T}_{0}}\]
C) \[2/3{{T}_{0}}\]
D) \[{{T}_{0}}\]
Correct Answer: A
Solution :
Let initial temperature and volume be \[{{T}_{0}}\] and \[{{V}_{0}}\]. Since the process is adiabatic, the first temperature and volume is \[T{{V}^{\gamma -1}}={{T}_{0}}V_{0}^{\gamma -1}\](\[\gamma =5/3\]for monoatomic gas) \[\therefore \] \[T={{T}_{0}}{{\left( \frac{{{V}_{0}}}{{{V}_{0}}/8} \right)}^{2/3}}=4{{T}_{0}}\]
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