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 `P_0` and temperature is `T_0`, atmospheric pressure is also `P_0`. Now the temperature of the gas is increased to `2T_0`, the tension in the wire will be

Options

A. `2P_0 A`
B. `P_0 A`
C. `(P_0 A)/(2)`
D. `4P_0 A`

Answer

B

Explanation

Since, V = constant `implies P prop T`
`T=2T_0 implies P=2P_0`
Let F be the tension in the wire
`F=(P-P_0)A =(2P_0-P_0)A=P_0A`