🔥 Gas gets hotter
The molecules move faster. They hit the walls harder and more often, so the pressure goes up.
Ideal Gas Molecules » Pressure and Temperature of a Gas
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 5.20, 5.21
- Why heating a gas in a sealed container raises its pressure, in terms of molecules
- That the pressure of a fixed amount of gas at constant volume is proportional to its Kelvin temperature
- How to use p1 / T1 = p2 / T2, with the temperatures in kelvin
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Unlock This CourseHeating a gas in a sealed container
Think of a car tyre on a hot day, or an aerosol can left in a hot car. The air inside cannot escape and the container hardly changes size. When the gas gets hotter, its pressure goes up. This is why aerosol cans carry a warning not to heat them.
In this lesson we look at a fixed amount of gas (a sealed sample, so no molecules get in or out) kept at constant volume, so only the temperature and the pressure change. The last lesson, Pressure and Volume of a Gas, did the opposite: it kept the temperature constant and changed the volume.
Key terms:
- Constant volume: the gas is in a rigid, sealed container, so the space it fills does not change.
Explaining the pressure and temperature link
You already know that a gas makes pressure because its molecules hit the walls of the container, and that the Kelvin temperature is linked to the average kinetic energy of the molecules (see Gas Molecules and Pressure and Absolute Zero and the Kelvin Scale). Now put the two ideas together. Warm a sealed flask of air and follow what happens:
- The temperature goes up, so the molecules move faster on average.
- Faster molecules cross the flask in less time, so they hit the walls more often.
- Each fast molecule also hits with a bigger force, so they hit the walls harder.
- The volume has not changed, so the area of the walls is the same. A bigger total force on the same area means a higher pressure.
❄️ Gas gets colder
The molecules move more slowly. They hit the walls less hard and less often, so the pressure goes down.
Compare this with the last lesson. When the volume got smaller at constant temperature, the molecules hit the walls more often but not harder. Here the molecules hit harder and more often.
Learn this
For a fixed amount of gas at constant volume, the pressure is proportional to the Kelvin temperature. If the Kelvin temperature doubles, the pressure doubles. If the Kelvin temperature halves, the pressure halves.
This only works with the Kelvin temperature. A gas does not double its pressure when the Celsius temperature doubles. The gas at 20 °C is not at "twice" the temperature of the gas at 10 °C, because 0 °C is not a true zero. Zero kelvin is, because the molecules have almost no kinetic energy there.
The equation p1 / T1 = p2 / T2
Because pressure is proportional to Kelvin temperature, dividing the pressure by the Kelvin temperature always gives the same answer. So we can compare the gas before and after a change:
Pressure and temperature of a fixed mass of gas
p1 / T1 = p2 / T2
p1 and T1 are the pressure and Kelvin temperature at the start. p2 and T2 are the pressure and Kelvin temperature at the end. This only works at constant volume.
You do not need to memorise this equation. It is printed on the formulae page of the exam paper. You do need to know how to use it.
Units
The temperatures must be in kelvin. Convert first, using K = °C + 273. Pressure can be in Pa or kPa, as long as you use the same unit for p1 and p2. The answer comes out in that unit.
Worked example 1: a sealed flask in a water bath
A sealed flask of air at 27 °C has a pressure of 100 kPa. It is placed in a water bath at 87 °C. The volume of the flask does not change. Calculate the new pressure of the air.
Step 1: Convert to kelvin: T1 = 27 + 273 = 300 K and T2 = 87 + 273 = 360 K
Step 2: Write the equation: p1 / T1 = p2 / T2
Step 3: Substitute: 100 / 300 = p2 / 360
Step 4: Multiply both sides by 360: p2 = 100 × 360 ÷ 300 = 120 kPa
Check: the gas got hotter, so the pressure should go up. 120 kPa is more than 100 kPa. ✅
Worked example 2: a car tyre
A car tyre has an air pressure of 210 kPa at 7 °C. After a long drive the air in the tyre is at 47 °C. Assume the volume of the tyre does not change. Calculate the pressure of the air in the tyre after the drive.
Step 1: T1 = 7 + 273 = 280 K and T2 = 47 + 273 = 320 K
Step 2: Substitute: 210 / 280 = p2 / 320
Step 3: p2 = 210 × 320 ÷ 280 = 240 kPa
Answer: 240 kPa. This is why tyre pressures are best checked when the tyres are cold.
Worked example 3: an aerosol can in a fire
An aerosol can contains gas at 240 kPa at 27 °C. The can bursts when the pressure reaches 720 kPa. Calculate the temperature, in °C, at which the can bursts. Assume the volume does not change.
Step 1: T1 = 27 + 273 = 300 K
Step 2: Substitute: 240 / 300 = 720 / T2
Step 3: Rearrange: T2 = 720 × 300 ÷ 240 = 900 K
Step 4: Convert back to °C: 900 − 273 = 627 °C
Check: the pressure tripled (240 to 720), so the Kelvin temperature should triple (300 to 900). ✅
Worked example 4: cooling a gas
A sealed container holds gas at 80 kPa and 127 °C. It is cooled to −73 °C. Calculate the new pressure.
Step 1: T1 = 127 + 273 = 400 K and T2 = −73 + 273 = 200 K
Step 2: Substitute: 80 / 400 = p2 / 200
Step 3: p2 = 80 × 200 ÷ 400 = 40 kPa
Answer: 40 kPa. The Kelvin temperature halved, so the pressure halved. The Celsius temperature did not halve, which is why using °C would give a wrong answer.
Suggested investigation (optional)
The spec also lists an optional suggested investigation into how the volume of a gas changes with temperature. You only need to know that it exists. There is no equation to learn for it in this course.
Common mistakes
- Using the temperatures in °C. Always convert to kelvin first.
- Adding 273 to one temperature but forgetting the other.
- Using the equation when the volume is changing. It only works at constant volume.
- Mixing units for pressure, such as kPa for p1 and Pa for p2.
- Explaining the rise in pressure with only "the molecules hit more often". For a gas that is heated, say that the molecules move faster, so they hit the walls harder and more often.
- Forgetting to check: if the gas is hotter, the pressure must be higher.
Exam-style question
A rigid, sealed metal container holds a fixed amount of gas at a pressure of 120 kPa and a temperature of 15 °C. The container is heated until the gas is at 75 °C.
(a) Explain, in terms of the molecules of the gas, why the pressure increases. [3 marks]
(b) Calculate the new pressure of the gas. [4 marks]
(c) State why the container must be rigid for your calculation to be correct. [1 mark]
Model answer
(a) The molecules move faster as the temperature rises (1). So they hit the walls harder (1) and more often (1), giving a bigger force on each unit area of the wall, so a higher pressure.
(b) T1 = 15 + 273 = 288 K and T2 = 75 + 273 = 348 K (1). p1 / T1 = p2 / T2, so 120 / 288 = p2 / 348 (1). p2 = 120 × 348 ÷ 288 (1). p2 = 145 kPa (1).
(c) The volume of the gas must stay constant (1).
Exam tip
Convert both temperatures to kelvin before you write anything else, and show the conversion. Even if you slip later, the marks for the conversion are easy to earn.