P1V1 = P2V2
Boyle's Law graph representing pressure inversely proportional to volume
V ∝ T
Charles's Law graph representing temperature (in °C) directly proportional to the volume
P ∝ T
Pressure Law graph representing temperature (in °C) directly proportional to the volume
The pressure inside a bicycle tyre is 5.10 × 105 Pa when the temperature is 279 K.After the bicycle has been ridden, the temperature of the air in the tyre is 299 K. Calculate the new pressure in the tyre, assuming the volume is unchanged.
Remember when using any ideal gas law, including the ideal gas equation, the temperature T must always be in kelvin (K)
pV ∝ T
Gas molecules move about randomly at high speeds
The frequency of collisions of the gas molecules per unit area of a container
Molecular model of the three ideal gas laws
An ideal gas is in a container of volume 4.5 × 10-3 m3.The gas is at a temperature of 30 °C and a pressure of 6.2 × 105 Pa.Calculate the pressure of the ideal gas in the same container when it is heated to 40 °C.
Step 1: Ideal gas relation between pressure, volume and temperature
pV ∝ T
Step 2: Write the equation in full
pV = kT
Step 3: Rearrange for the constant of proportionality
Step 4: Convert temperature T into Kelvin
θ °C + 273.15 = T K
30 °C + 273.15 = 303.15 K
Step 5: Substitute in known value into constant of proportionality equation
Step 6: Rearrange ideal gas relation equation for pressure
Step 7: Substitute in new values
k = 9.203...
V stays the same = 4.5 × 10-3 m3
T = 40 °C = 40 + 273.15 = 313.15 K
Don’t round too early in your working out! In the worked example, the unrounded value of k is represented by “…” to show its full value is to be carried over to the next step of the calculation. On your calculator, this can be done by using the “ans” button instead of typing in the whole number.
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