The diagram below shows the relative equilibrium positions of a piston, of negligible mass, in a container of air, at different temperatures.
Using the kinetic model of matter,
(i) explain why the piston at 25 °C does not sink to the bottom of the container.
(ii) calculate the pressure of the gas at 25 °C
(iii) calculate the pressure exerted by the gas at 50 °C
(iv) explain the reason the piston rises to a greater equilibrium height at 50 °C
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Answer:
(i) The particles of air collide with the surface of the container, as well as the surface of the piston, and hence exerts a upward force on the piston. This prevents it from sinking to the bottom.
(ii) Since the piston is of negligible mass, it exerts negligible force on the air in the container.
Since the piston is in equilibrium,
pressure of gas = pressure of atmosphere
= 1.0 х 105 Pa
(iii) Since the piston is still in equilibrium,
pressure of gas = pressure of atmosphere
= 1.0 х 105 Pa
(iv) As the temperature is greater, the kinetic energy of the particles is greater. This increases the pressure of the gas, hence causing a net upwards force on the piston, causing the piston moves upwards.
As the piston moves upwards, the volume of the air increases, causing a corresponding reduction in the gas pressure according to Boyle's Law (P1V1 = P2V2). This continues until equilibrium is reached, when pressure of the gas equals the pressure of the atmosphere.
The end result is the greater equilibrium height for temperature at 50 °C
