2022 A/L Physics Past Paper · Question 15 (English Medium)

Answer: (2) Only (C) is true.

What the question asks

We want: which of the statements (A), (B), (C) are true about absolute zero.

What each letter means:

$T$ ($\text{K}$): the temperature on the absolute scale.

$m$ ($\text{kg}$): the mass of one gas molecule.

$\overline{c^2}$ ($\text{m}^2\ \text{s}^{-2}$): the mean square speed of the molecules.

$R$ ($\text{J mol}^{-1}\ \text{K}^{-1}$): the universal gas constant.

$M$ ($\text{kg mol}^{-1}$): the molar mass of the gas.

Relevant theory

The value of temperature at O' is -273.15 °C (in celsius).

known as absolute zero to that temperature.

when M is constant, r.m.s speed depends on T.

Reading the options

The options are combinations of (A), (B) and (C).

We test each statement on its own.

For example, think of marbles in a shaken tray.

Shake the tray harder and the marbles move faster. Shake it gently and they move slowly.

If you stop shaking completely, every marble stops. That is what absolute zero is for gas molecules: the lowest possible state, where the motion has stopped.

For a gas, the speed of the molecules is tied to the temperature.

$$\overline{c^2} = \dfrac{3RT}{M}$$

In words: the mean square speed is $3RT$ divided by the molar mass.

The mean kinetic energy of one molecule is $\dfrac{1}{2}m\overline{c^2}$. So it is proportional to $T$.

Reasoning and calculation

It is the temperature at which water freezes at atmospheric pressure.

Water freezes at $0\ ^\circ\text{C}$. In kelvin that is $273.15\ \text{K}$. The book gives absolute zero as $-273.15\ ^\circ\text{C}$, a very different temperature.

A

It is the temperature at which all gases become liquids.

Real gases turn into liquids at temperatures well above absolute zero. The book defines absolute zero as the zero of the thermodynamic scale, not as the point where all gases liquefy.

B

It is the temperature at which the mean kinetic energy of an ideal gas becomes zero.

At $T = 0$ the equation gives $\overline{c^2} = 0$. The molecules of an ideal gas have no speed, so their mean kinetic energy $\dfrac{1}{2}m\overline{c^2}$ is zero.

C

Statement (A) is false: absolute zero is $-273.15\ ^\circ\text{C}$, not the freezing point of water.

Statement (B) is false: gases liquefy well above absolute zero.

Statement (C) is true: $\overline{c^2} = \dfrac{3RT}{M}$ becomes zero at $T = 0$, so the mean kinetic energy is zero.

So only (C) is true.

Why the other options fail

Statement (A) is false. Water freezes at $273.15\ \text{K}$. Statement (C) is true.

Statement (A) is false. Water freezes at $273.15\ \text{K}$, not at absolute zero.

Statement (B) is false. Gases turn to liquids well above absolute zero. The speed of the molecules depends on $T$, not on liquefying.

Statements (A) and (B) are false. Only (C) is true.

Conclusion

Only statement (C) is true. The mean kinetic energy of an ideal gas becomes zero at absolute zero.

The answer is (2).

Absolute zero is the zero of the kelvin scale, $-273.15\ ^\circ\text{C}$.

At $T = 0$ the molecules of an ideal gas have no kinetic energy.

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