At constant volume, you cool a sealed, air-filled can, and the pressure reduces by half. What happens in this situation? The number of collisions per unit area doubles. The spaces between the gas molecules shrink. The temperature of the air inside reduces by half. Half of the gas leaks out.

Question

Chemistry

Khalil Atkins

19 August, 05:54

At constant volume, you cool a sealed, air-filled can, and the pressure reduces by half. What happens in this situation? The number of collisions per unit area doubles. The spaces between the gas molecules shrink. The temperature of the air inside reduces by half. Half of the gas leaks out.

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Answers (1)

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Damian Townsend · Answer 1

The correct answer to the question is

The temperature of the air inside reduces by half.

Explanation:

The relation to apply here is

(P₁*V₁) / T₁ = (P₂*V₂) / T₂

Thus we have at constant volume

P₁/T₁ = P₂/T₂

Therefore since the pressure reduces by half we have

then P₂ = 0.5 * P₁ or

P₁/T₁ = 0.5 * P₁/T₂ that is 1/T₁ = 0.5/T₂ or T₂ = 0.5 * T₁

The temperature of the air reduces by half

The above relationship is an example of Gay-Lussac's law which states that constant volume, the pressure of a given mass of gas is directly proportional to the temperature in kelvin. That is an increase in presure increases the temperature and a decrease in pressure causes an equivalent decrease in temperature