A cylinder made of perfectly non conducting material closed at both 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°C and pressure P0 = 1 atm. Now if the gas in one of the parts is slowly heated to t = 57°C while the temperature of other part is maintained at t0 the distance moved by the piston in cm from the middle of the cylinder will be(length of the cylinder = 84 cm)

InitiallyFinallyFor left partP0LAT0=P1(L+x)AT∴P1=P0LT0TL+x=P0LL+x330300----1A = area of cross section of piston For right partP0 LA = P2 (L - x) A∴P2=P0LL−x---2P1=P2⇒ x=L21=2cm.

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A cylinder made of perfectly non conducting material closed at both 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 $t_{0} = 27 ° C$ and pressure P₀ = 1 atm. Now if the gas in one of the parts is slowly heated to t = 57°C while the temperature of other part is maintained at t₀ the distance moved by the piston in cm from the middle of the cylinder will be
(length of the cylinder = 84 cm)

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Detailed Solution

Initially
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Finally

For left part
$\begin{array}{l} \frac{P_{0} LA}{T_{0}} = \frac{P_{1} (L + x) A}{T} \\ ∴ P_{1} = \frac{P_{0} L}{T_{0}} \frac{T}{L + x} = \frac{P_{0} L}{L + x} \frac{330}{300} - - - - (1) \end{array}$
A = area of cross section of piston

For right part
P₀ LA = P₂ (L - x) A
$\begin{array}{l} ∴ P_{2} = \frac{P_{0} L}{L - x} - - - (2) \\ P_{1} = P_{2} \\ \Rightarrow x = \frac{L}{21} = 2 cm . \end{array}$