❄️ Colder gas
The Kelvin temperature goes down, so the average kinetic energy of the molecules goes down and they move more slowly on average.
Ideal Gas Molecules » Absolute Zero and the Kelvin Scale
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 5.16, 5.17, 5.19
- Why nothing can be colder than absolute zero, −273 °C
- How the Kelvin scale works and how to convert between kelvin and degrees Celsius
- Why the Kelvin temperature of a gas is proportional to the average kinetic energy of its molecules
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Unlock This CourseWhy there is a coldest possible temperature
In the lesson Gas Molecules and Pressure you saw that cooling a gas makes its molecules slow down. Their kinetic energy goes down, and so does their average speed. Now think about cooling a gas more and more.
The molecules move more and more slowly. Eventually they would have the least possible energy. They cannot have less than that, so they cannot slow down any further, and the gas cannot get any colder. This lowest possible temperature is called absolute zero. It is −273 °C.
You can also see this from the pressure of a gas. Take a fixed amount of gas in a sealed container that cannot change size. Measure its pressure at different temperatures. As the gas cools, the pressure falls, because the slower molecules hit the walls less often and with less force. If you plot pressure against temperature in °C, the points lie on a straight line sloping upwards. Now extend this line backwards, past the lowest temperature you measured. The line reaches zero pressure at −273 °C. Zero pressure means the molecules are no longer hitting the walls. That is the lowest energy they can have.
Key terms:
- Absolute zero: the lowest possible temperature, −273 °C. Nothing can be colder.
- Kelvin scale: a temperature scale that starts at absolute zero. Temperatures on it are measured in kelvin (K).
The Kelvin scale
The Celsius scale is based on water: 0 °C is where ice melts and 100 °C is where water boils. Because it is based on water, it can have negative numbers. The Kelvin scale is different. It starts at absolute zero, so 0 K is the coldest possible temperature.
A change of 1 kelvin is exactly the same size as a change of 1 °C. So a gap of 10 °C between two temperatures is also a gap of 10 K. The two scales only differ in where they start. To convert, you add or subtract 273.
Converting between the scales
temperature in kelvin (K) = temperature in °C + 273
temperature in °C = temperature in kelvin (K) − 273
Because 0 K is the coldest possible temperature, there are no negative kelvin temperatures. A temperature on the Kelvin scale is never below zero.
Notice that the unit is written as K, not °K. We say "300 kelvin" and write 300 K, with no degree sign.
| Situation | Temperature in °C | Temperature in K |
|---|---|---|
| Absolute zero | −273 | 0 |
| Ice melting | 0 | 273 |
| A cool room | 20 | 293 |
| Water boiling | 100 | 373 |
Worked example 1: Celsius to kelvin
Convert 25 °C to kelvin.
Step 1: Write the relationship: temperature in K = temperature in °C + 273
Step 2: Substitute: temperature in K = 25 + 273
Step 3: Answer: 298 K
Worked example 2: kelvin to Celsius
The surface of a frozen pond is at 263 K. What is this in °C?
Step 1: Write the relationship: temperature in °C = temperature in K − 273
Step 2: Substitute: temperature in °C = 263 − 273
Step 3: Answer: −10 °C
Worked example 3: a temperature change
A gas is warmed from 280 K to 310 K. What is the temperature change in °C?
Step 1: A kelvin is the same size as a degree Celsius, so the change is the same on both scales.
Step 2: 310 − 280 = 30
Step 3: Answer: the temperature rises by 30 K, which is 30 °C.
Kelvin temperature and the energy of molecules
The Kelvin scale starts where the molecules would have the least possible energy. That makes it the natural scale for gases. For a gas, the Kelvin temperature is proportional to the average kinetic energy of its molecules.
Learn this
The Kelvin temperature of a gas is proportional to the average kinetic energy of its molecules.
Proportional means that if one quantity doubles, the other doubles too. If you halve one, you halve the other. So:
- If the Kelvin temperature of a gas doubles, the average kinetic energy of its molecules doubles.
- If the Kelvin temperature is three times bigger, the average kinetic energy is three times bigger.
- At 0 K the molecules would have the least possible energy.
This only works with kelvin. It does not work with degrees Celsius. A gas at 10 °C does not have half the energy of a gas at 20 °C, because 0 °C is not a point of zero energy. To compare energies, convert to kelvin first.
Worked example 4: doubling the energy
A gas is at 0 °C. To what temperature in °C must it be heated so that the average kinetic energy of its molecules doubles?
Step 1: Convert to kelvin: 0 + 273 = 273 K
Step 2: The kinetic energy doubles when the Kelvin temperature doubles: 273 × 2 = 546 K
Step 3: Convert back: 546 − 273 = 273 °C
Answer: 273 °C. Doubling the number in °C would not work: 0 °C doubled is still 0 °C.
🔥 Hotter gas
The Kelvin temperature goes up, so the average kinetic energy of the molecules goes up and they move faster on average.
Common mistakes
- Writing °K instead of K. The unit is the kelvin, K.
- Adding 273 when you should subtract it, or the other way round. Check your answer: the Kelvin number is always bigger than the Celsius number.
- Writing a negative temperature in kelvin. The Kelvin scale has no negative values.
- Saying that doubling the temperature in °C doubles the kinetic energy. Convert to kelvin first.
- Thinking a kelvin is a different size from a degree Celsius. They are the same size.
Exam-style question
(a) State the temperature of absolute zero in °C. [1 mark]
(b) Explain why it is impossible for a gas to be cooled below absolute zero. [2 marks]
(c) A gas has a temperature of 27 °C. Calculate its temperature in kelvin. [1 mark]
(d) The temperature of this gas is raised to 600 K. Calculate how many times bigger the average kinetic energy of its molecules is. [2 marks]
Model answer
(a) −273 °C (1)
(b) Cooling a gas slows its molecules, so they lose kinetic energy (1). At absolute zero they have the least possible energy, so they cannot slow down or lose any more energy (1).
(c) 27 + 273 = 300 K (1)
(d) The Kelvin temperature is proportional to the average kinetic energy (1). 600 ÷ 300 = 2, so the average kinetic energy is 2 times bigger (1).
Exam tip
In any question that compares the energy of molecules at two temperatures, convert both temperatures to kelvin before you do anything else. Writing "+ 273" on the first line of your working shows the examiner you know what you are doing.