Question

A cylinder made of perfectly non conducting material closed at bottle ends is divided into two equal parts by a heat proof piston. Both parts of the cylinder contain the same masses of a gas at a temperature $t_0={27}^{\circ }$ and pressure $P_0=1$ atm. Now if the gas in one of the parts is slowly heated to $t={57}^{\circ }$ while the temperature of first part is maintained at $t_0$ the distance moved by the piston from the middle of the cylinder will be ( length of cylinder = 84 cm)

• A. 3cm
• B. 5cm
• C. 2cm
• D. 1cm

Answer 1

The correct option is C 2cm

Let the final pressure be $P$ and distance moved by piston be x

Then applying ideal gas eqn. on the 2 compartments,

$P\times (42-x)=1\times 42$ ........(i)

$\frac{P\times (42+x)}{330}=\frac{42}{300}\Rightarrow P\times (42+x)=11/10\times 42$ .........(ii)

Solving eqn. (i) and (ii), x=2cm