In a cylindrical container of sufficiently large height, two easily moving pistons enclose a certain amount of the same ideal gas in two chambers as shown in Figure 2.43. The upper piston is at a heig

Question

In a cylindrical container of sufficiently large height, two easily moving pistons enclose a certain amount of the same ideal gas in two chambers as shown in Figure 2.43. The upper piston is at a height 20 cm from the bottom and the lower piston is at a height 8 cm from the bottom. The mass of each piston is $m$ kg and the cross-sectional area of each piston is $A$ $m^{2}$ , where $\frac{m g}{A} = P_{0}$ and $P_{0}$ is the atmospheric pressure = $1 \times 1 0^{5}$ N/ $m^{2}$ . The cylindrical container and pistons are made of conducting material. Initially the temperature of the gas is $2 7^{\circ}$ C and the whole system is in equilibrium. Now the upper piston is slowly lifted by 16 cm and held in that position with the help of some external force. As a result, the lower piston rises slowly by $l$ cm.

The value of $l$ is:

TestHub · Accepted Answer

Initially the upper chamber is at 2 P 0 ​ (12 cm tall) and the lower chamber at 3 P 0 ​ (8 cm tall). Finally the upper height is 28 − l and the lower is 8 + l . Boyle gives P u ​ = 28 − l 24 P 0 ​ ​ and P l ​ = 8 + l 24 P 0 ​ ​ = P u ​ + P 0 ​ . Trying l = 4 : 2 P 0 ​ = P 0 ​ + P 0 ​ . B.

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