Introductory physics: those ol’ gas laws

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?


Filed under Introductory physics

5 responses to “Introductory physics: those ol’ gas laws

  1. sludgejudge

    I’m not a physics guy but here’s my theory.
    At the point where the tire contacts the road there is a very small flat spot. As the tire rolls the location of the flat spot changes causing the rubber to flex, along with steel belts in some cases. This flexing causes heat-like when you repeatedly bend a paperclip. The heat from flexing increases the gas temperature, and since the volume in the tire is pretty much fixed, the pressure increases. The increased temperature makes the rubber more flexible, and a little weaker, which, in combination with the increased pressure, makes a blowout more likely. Best wishes from Florida.

  2. cormac

    A good answer! I have always assumed it’s simply because the heating effect of friction acts on a volume of air that is fixed (as the rubber doesn’t expand much) and therefore the air pressure builds up until the tyre blows!
    However, it’s certainly posssible that the rubber itself plays a role, I must ask a mechanic

    • sludgejudge

      I’m a civil engineer and worked in a service station when I was going to college (a long time ago). I changed a bunch of tires and they were aways very warm. Originally, I thought that the heat was the result of friction, and slippage, between the tire and road, but it seems that tires would wear out very quickly if this were the case. I thought about the friction between the tire and air, both inside and outside of the tire, but the viscosity of air is so low that it’s hard to generate much heat, plus the external movement of air with respect to the tire tends to dissipate heat. That left me with the “flexing due to distortion” theory. Thanks for the reply. I enjoy reading your stuff.

  3. zhela

    if i wana to do this expirement in the lab.
    mean boyles law so what will i do in the first step