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A cylindrical glass of height h = 10 cm was covered with a piston of mass 3.5 kg and has a cross sectional area of 450 cm2.

(i) Determine the pressure that is exerted by this piston on the gas in the chamber, as shown in the figure. Assume gravitational acceleration 'g' to be 9.81 m/s2. (3)
(ii) Determine the work done when the same cylinder is heated afterwards at a constant pressure of 1 atm and its initial volume changes from Vo to 3Vo. (3)

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Answer:

(i) The pressure exerted by the piston on the gas in the chamber can be calculated using the formula:

Pressure = Force / Area

The force exerted by the piston on the gas is equal to its weight, which can be calculated as:

Force = mass x gravitational acceleration

= 3.5 kg x 9.81 m/s^2

= 34.335 N

The area of the piston is 450 cm^2, which is equal to 0.045 m^2.

Therefore, the pressure exerted by the piston on the gas is:

Pressure = Force / Area

= 34.335 N / 0.045 m^2

= 763 N/m^2 or 763 Pa

(ii) The work done when the cylinder is heated at a constant pressure of 1 atm can be calculated using the formula:

Work = Pressure x Change in Volume

The initial volume of the cylinder is Vo, and the final volume is 3Vo. Therefore, the change in volume is:

Change in Volume = 3Vo - Vo

= 2Vo

The pressure is given as 1 atm, which is equal to 101,325 Pa.

Therefore, the work done is:

Work = Pressure x Change in Volume

= 101,325 Pa x 2Vo

= 202,650 Pa.Vo or 202,650 J:

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