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Question
Explain, on the basis of the kinetic theory of gases, how the pressure of a gas changes if its volume is reduced at a constant temperature.
Solution 1
- At constant temperature, a gas's average kinetic energy per molecule remains constant.
- When a gas's volume is lowered at a constant temperature, the number of gas molecules colliding with the container's walls per unit time increases.
- The momentum transferred per unit time per unit area, i.e. the force exerted by the gas on the walls, increases as a result.
- As a result, the gas pressure rises.
Solution 2
Let P - be the pressure exerted by the gas
V - be the volume of the gas
N - be the number of molecule of gas
m - be the mass of each molecule of gas.
∴ Total mass of the gas, M = Nm.
From kinetic theory of gases,
`P = (1/3) (Nm)/V barv^2`
∴ Pressure exerted by gas in an enclosed vessel is
`P = 2/3 N/V (1/2mbarv^2)`
But `1/2mbarv^2` = (Kinetic energy at constant temperature)
N is number which is also constant.
∴ `P = "Constant"/V`
∴ `P ∝ 1/V`
As a result, at constant temperature, increasing the pressure of the gas reduces its volume.
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