A nice way to finish our section on heat and temperature is to look at the so-called gas laws. The Ideal Gas Law is a famous equation that relates the pressure P, volume V and temperature T of a given gas by the very neat expression
PV/T = nR
where n is the number of moles of a gas and R is a constant known as the Rydberg constant.
For a physicist, the details of the right hand side of the equation is of little interest. What is important is that it is constant i.e. the product [pressure x volume divided by temperature] of a given gas remains fixed. Hence if any one (or all) of these three variables is changed, the others must adjust such that the total product remains the same.
The ideal gas law embodies three separate gas laws that were discovered by experiment many years ago. For example, you can see from the equation that if the temperature of a gas is held constant (isothermal process), the product of PV must remain constant. Hence the volume of a gas decreases with increasing pressure if the gas is held at a steady temperature – a law known as Boyle’s Law after the Irish scientist who first discovered it in the 17th century.
Boyle’s Law – a favourite 1st year experiment
On the other hand, you can see from the equation that if the pressure of a gas is held constant (isobaric process) the quotient V/T must remain constant. Hence the volume of a gas must increase linearly with increasing temperature if the pressure is held fixed – a law known as Charle’s law after the English scientist who first observed it (also known as thermal expansion).
Charle’s Law: volume increases with temp at constant pressure
Finally, if you increase the temperature of a gas while keeping the volume fixed the quotient P/T must remain constant. Here the pressure of a gas must increase linearly with increasing temperature, a process known as an isovoluic process. This process is the most dangerous one of the three, as pressure can build up unobserved and cause a nasty explosion.
Press increases with temp at constant volume: this can be used to estimate the temperature of Absolute Zero
Each of the three laws above were discovered empirically, many years ago. Later, when the molecular structure of gases was understood, the ideal gas law, embodying all three laws, was derived from first principles from the kinetic theory of gases. This was a stunning achievment and marks one of the first unifications of the laws of physics.
When a car is driven at speed, the risk of a tyre blowout is much larger than normal. Can you explain why in the context of the ideal gas law?