What is the ratio of work done by the gas in moving the piston from the initial | TestHub

Passage / Comprehension

A mass less piston, which can move without friction, closes a sample of Helium in a vertical, thermally insulated cylinder, which is closed at its bottom, and the cross-section of which is $A = 2 dm^{2}$ . Above the piston there is a fixed stand to which an unstretched spring of spring constant 2000 N/m is attached, whose bottom end is at a distance of 2 dm from the piston when the volume of the gas is $V_{0} = 8 dm^{3}$ . The external pressure is $p_{0} = 1 0^{5}$ Pa, $g = 10 m/s^{2}$ . The gas confined in the cylinder is heated with an electric heating element. (1 dm $= 1 0^{- 1}$ m)

What is the ratio of work done by the gas in moving the piston from the initial position to A, and from there to B?

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Answer:

Solution:

$P_{B} = P_{0} + \frac{k x}{A} = 1 0^{5} + \frac{2000 \times 2 \times 1 0 ^{- 1}}{2 \times 1 0 ^{- 2}} = 1.2 \times 1 0^{5}$ Pa.

Up to A: $W_{1} = 1 0^{5} \times 4 \times 1 0^{- 3} = 400$ J.

From A to B: $W_{2} = \frac{( 1.0 + 1.2 ) \times 1 0 ^{5}}{2} \times 4 \times 1 0^{- 3} = 440$ J.

$\frac{W _{1}}{W _{2}} = \frac{400}{440} = \frac{10}{11}$ .

Physics - Heat & Thermo Question with Solution | TestHub

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