question_answer

A cylindrical tube of uniform cross-sectional area A is fitted with two air tight frictionless pistons. The pistons are connected to each other by a metallic wire. Initially the pressure of the gas is P0 and temperature is T0, atmospheric pressure is also P0. Now the temperature of the gas is increased to 2T0, the tension in the wire will be

A)            \[2{{P}_{0}}A\]                    

B)            \[{{P}_{0}}A\]

C)            \[\frac{{{P}_{0}}A}{2}\]   

D)            \[4{{P}_{0}}A\]

Correct Answer: B

Solution :

                   Volume of the gas is constant V = constant \ \[P\propto T\] i.e., pressure will be doubled if temperature is doubled                    \ \[P=2{{P}_{0}}\]                                       Now let F be the tension in the wire. Then equilibrium of any one piston gives            \[F=(P-{{P}_{0}})A=(2{{P}_{0}}-{{P}_{0}})A={{P}_{0}}A\]