Thermodynamics Question 259
Question: A monatomic ideal gas, initially at temperature $ T _{1} $ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $ T _{2} $ by releasing the piston suddenly. If $ L _{1} $ and $ L _{2} $ are the length of the gas column before and after expansion respectively, then $ \frac{T _{1}}{T _{2}} $ is given by
Options:
A) $ {{( \frac{L _{1}}{L _{2}} )}^{2/3}} $
B) $ \frac{L _{1}}{L _{2}} $
C) $ \frac{L _{2}}{L _{1}} $
D) $ {{( \frac{L _{2}}{L _{1}} )}^{2/3}} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Here $ T{{V}^{^{\gamma -1}}}=\text{constant} $
As $ \gamma =\frac{5}{3}, $ hence $ T{{V}^{2/3}}=\text{constant} $
Now $ T _{1}L _{1}^{2/3}=T _{2}L _{2}^{2/3}\text{ (}\therefore V\propto L\text{)} $ ;
Hence, $ \frac{T _{1}}{T _{2}}={{( \frac{L _{2}}{L _{1}} )}^{2/3}} $
