A cylindrical tube of uniform cross-sectional area A is fitted with...

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

2 T_0

, the tension of wire will be A cylindrical tube of uniform cross-sectional area A is fitted with two air tight frictionless pistons. The pistons are

A cylindrical tube of uniform cross-sectional area A is fitted with two air tight frictionless pistons. The pistons are

Options

A $2 p_0 A$
B $p_0 A$
C $\frac{p_0 A}{2}$
D $4 p_0 A$

Correct answer

B. $p_0 A$

Step-by-step solution

Volume of the gas is constant i.e.

V

= constant

\therefore p \propto T

i.e. pressure will be doubled if temperature is doubled. A cylindrical tube of uniform cross-sectional area A is fitted with two air tight frictionless pistons. The pistons are

Let

F

be the tension in the wire. Then, equilibrium of any one pipes gives.

F=\left(p-p_0\right) A=\left(2 p_0-p_0\right) A=p_0 A

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