Temperature and ideal gases

What the syllabus demands

• —Use the thermodynamic (kelvin) scale: T/K = θ/°C + 273.15
• —Use the equation of state pV = nRT (and pV = NkT)
• —Recall the kinetic theory result pV = ⅓Nm<c²> and relate mean kinetic energy to temperature
• —Define internal energy as the sum of random kinetic and potential energies of the molecules
• —Apply the first law of thermodynamics: ΔU = q + W

Definitions that earn marks

Clear definitions to practise — check your course mark scheme

Ideal gas

A gas that obeys pV = nRT at all pressures and temperatures — assuming negligible molecular volume and no intermolecular forces except during collisions.

Internal energy

The sum of the random kinetic energies and potential energies of all the molecules of a system. For an ideal gas, the potential term is zero, so internal energy depends only on temperature.

First law of thermodynamics

The increase in internal energy of a system equals the heat supplied to it plus the work done on it: ΔU = q + W.

Absolute zero

0 K (−273.15 °C): the temperature at which molecules have minimum internal energy.

The equations

More equations to practise: the Edexcel IAL formula sheet.

Where the marks die

Common mistakes to check

1. 01

   Celsius in gas equations. Every temperature in pV = nRT and E = 3/2 kT must be in kelvin. Using 25 instead of 298 is the most common zero on the topic.

2. 02

   Sign errors in the first law. In ΔU = q + W, W is work done ON the gas: compression is positive, expansion is negative. Read the convention off the formula sheet and state it.

3. 03

   Saying molecules have zero energy at 0 K — the syllabus wording is minimum internal energy.

4. 04

   Mean square speed handled as if it were the square of the mean speed. <c²> is averaged after squaring; its square root (the r.m.s. speed) is what E = ½m<c²> connects to temperature.

One worked example, done properly