Question

The figure shows a horizontal cylinder with two sections of unequal cross-section in which two points of area $A_{1}$ and $A_{2}$ can move freely. The pistons are joined together with an inextensible string and the space between the pistons is filled with an ideal gas. The whole system is in equilibrium.

If the gas is heated, in which direction will the pistons move?

Question Image

If the atmospheric pressure is $p_{0}$ , then determine the pressure of the gas.

Accepted Answer

Given, Area f cross section of both the pistons are $A_{1}$ and $A_{2}$

Let $p$ be the pressure of the gas and $F$ be the tension in the string.

Then, considering the equilibrium of each piston,

For piston $I$ , ${pA}_{1} = p_{0} A_{1} + F$

$\Rightarrow p = p_{0} + \frac{F}{A_{1}} . . . (i)$

For piston $II$ , ${pA}_{2} = p_{0} A_{2} + F$

$p = p_{0} + \frac{F}{A_{2}} . . . (ii)$

From Eqs. $(i)$ and $(ii)$ , if $A_{1} \neq A_{2}$ then the gas may have unique value of pressure only if tension in the string is zero, i.e., $F = 0$ . Thus, pressure of the gas is also atmospheric, $p = p_{0}$ .

B M Sharma Solutions for Chapter: Kinetic Theory of Gases, Exercise 1: ILLUSTRATIONS

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Kinetic Theory of Gases, Exercise 1: ILLUSTRATIONS

Questions from B M Sharma Solutions for Chapter: Kinetic Theory of Gases, Exercise 1: ILLUSTRATIONS with Hints & Solutions

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