2019 A/L Physics Past Paper · Question 13 (English Medium)

Dew point in a closed container

Consider the following statements regarding the dew point of air having water vapour in a closed container.

(A) At dew point, unsaturated water vapour becomes saturated water vapour.

(B) If the temperature is reduced below the dew point, some of the vapour will condense.

Which of the above statements is/are correct?

(1) Only A
(2) Only B
(3) Only A and B
(4) Only A and C
(5) All A, B, and C

Answer and explanation

Answer: (3) Only A and B

What the question asks

We want:

Which of the statements A, B and C are correct.

They are about a closed container of air with water vapour.

Relevant theory

The absolute humidity is the mass of water vapour in $1\ \text{m}^3$ of air.

Air can hold only so much vapour. The most it can hold is the saturated vapour density $\rho_s$ .

$\rho_s$ depends on the temperature only.

The dew point is the temperature where the vapour in the air just reaches this limit.

The temperature at which the volume of air gets saturated for the first time with water vapour existing in it, is known as the dew point of that volume of air.

Reading the options

The options are: only A, only B, A and B, A and C, or all three.

We test A, B and C one by one.

Reasoning and calculation

At the dew point, unsaturated vapour becomes saturated

This is the dew point. The vapour density in the air reaches $\rho_s$ . So the vapour is saturated.

Cooling below the dew point makes vapour condense

Below the dew point, $\rho_s$ gets smaller. The air cannot hold all the vapour. The extra vapour condenses into drops.

Reducing the volume lowers the absolute humidity

At the dew point the vapour is already saturated. If the volume is reduced, some vapour condenses. The vapour left stays at $\rho_s$ of the same temperature. So the absolute humidity does not fall. It stays the same.

$12.8$

$\rho = \rho_s(15^\circ\text{C})$

$25.6$

$\frac{12.8}{0.5}$

$6.4$

$12.8 - 12.8 \times 0.5$

Statement C is wrong.

The total mass of vapour falls. The volume falls in the same ratio.

So the mass in $1\ \text{m}^3$ stays $12.8$ g.

Only A and B are correct.

Why the other options fail

This option leaves out B. B is also correct.

This option leaves out A. A is also correct.

This option includes C. C is not correct. B is also left out.

This option includes C. C is not correct.

Conclusion

A and B are correct.

C is wrong. The absolute humidity stays at $\rho_s$ .

So the answer is option (3).

Thinking that the absolute humidity always falls when vapour condenses.

It falls when cooling makes $\rho_s$ fall. It does not change when pressing makes vapour condense at the same temperature.

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