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 t0 - 27 - and pressure P0 - 1 atm- Now if the gas in one of the parts is slowly heated to t - 57 - while the temperature of first part is maintained at t0 the distance moved by the piston from the middle of the cylinder will be length of cylinder - 84 cm

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Ideal Gas Equation

A cylinder ma...

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)

3cm

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5cm

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2cm

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1cm

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Solution

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

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The correct option is C 2cmLet the final pressure be P and distance moved by piston be xThen applying ideal gas eqn. on the 2 compartments,P×(42−x)=1×42 ........(i)P×(42+x)330=42300⇒P×(42+x)=11/10×42 .........(ii)Solving eqn. (i) and (ii), x=2cm