question_answer

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:

A) \[\frac{3}{8}{{T}_{0}}\]                     

B) \[\frac{3}{4}{{T}_{0}}\]

C) \[\frac{11}{8}{{T}_{0}}\]        

D) \[\frac{13}{8}{{T}_{0}}\]

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 \[{{T}_{0}}.\]