Question

Figure shows a cylindrical tube of cross-sectional area A filled with two frictionless pistons. The pistons are connected through wire. The tension in the wire if the temperature rises from T${}_0$ to 2T${}_0$ is (Initial pressure is P${}_0$, atmospheric pressure)

• A. $P_{0}A$
• B. $\frac{P_{0}A}{2}$
• C. $2P_{0}A$
• D. $\frac{2P_{0}A}{3}$

Answer 1

Answer: (A)

$P_{0}A$

Since the wired would be taut, there would be no change in the volume of enclosed gas, so $\frac{P}{T}=constant$

$⟹\frac{P}{2T_0}=\frac{P_0}{T_0}$

$⟹P=2P_0$

Thus, an equilibrium to exist, the difference in inside and outside forces must be balanced by the tension in the wire.

Thus, $T=2P_{0}A-P_{0}A=P_{0}A$