Thermodynamics Question 338
Question: Direction: An ideal diatomic gas is confined in a cylinder A of volume $ V _{0}, $ this cylinder is connected to another cylinder B with the help of tube of a negligible volume. The cylinder B is fitted with a movable piston which can be adjusted from outside. Initially, the piston is adjusted so that volume of B is the same as volume of A i.e., $ V _{0} $ . B is evacuated and the stopcork is opened so that gas expands and occupies the volume $ 2V _{0} $ . [System is thermally isolated from the surroundings].
Work done on the gas is [for n moles of gas]
Options:
A) $ nRT\ln 2 $
B) $ -nRT\ln 2 $
C) $ nRT $
D) $ -nRT $
Show Answer
Answer:
Correct Answer: A
Solution:
[a]During compression, process is slow so it is isothermal at constant temperature T.
So, work done,
$ W=nRT\ln \frac{V _{f}}{V _{i}}=-nRT\ln 2 $
This is the work done by the system on the surrounding, so work done by the surroundings on the system in nRT ln 2.
