Kinetic Theory Of Gases Question 17
Question: The air tight and smooth pistons of a cylindrical vessel are connected with a string, as shown. Initially,, pressure and temperature of the gas are $ p _{0} $ and $ T _{0} $ . The atmospheric pressure is also $ p _{0} $ . At a later time, tension in the string is $ \frac{3}{8}p _{0}A $ where A is the cross-sectional are of the cylinder. At this time, the temperature of the gas has become:
Options:
A) $ \frac{3}{8}T _{0} $
B) $ \frac{3}{4}T _{0} $
C) $ \frac{11}{8}T _{0} $
D) $ \frac{13}{8}T _{0} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ T+P _{0}A=PA $
$ T=(P-P _{0})A=\frac{3}{8}P _{0}A $ (given) $ P=\frac{3}{8}P _{0}+P _{0}=\frac{11}{8}P _{0} $ Now volume is constant by string So. $ P\propto T $ Initial temperature is $ T _{0}. $
BETA
