What is thermodynamics?
Thermodynamics is the part of physics that studies heat, work and temperature, and how energy changes form. It looks at big things (a gas in a cylinder, an engine, a fridge), not at single molecules.
The thing we study is called the system (for example, the gas). Everything around it is the surroundings. The boundary between them is a wall.
- Adiabatic wall: a perfect insulator. No heat can pass.
- Diathermic wall: a conducting wall. Heat can pass.
Thermal equilibrium
Put a hot body and a cold body in contact through a diathermic wall. Heat flows from the hot one to the cold one. The hot one cools, the cold one warms.
After some time both have the same temperature. Then heat stops flowing and the pressure, volume and temperature of each body stop changing. This state is called thermal equilibrium.
In short: two bodies are in thermal equilibrium when they have the same temperature.
Equilibrium in thermodynamics means the big (macroscopic) quantities do not change with time. Molecules still move inside, but their average behaviour stays the same.
The zeroth law of thermodynamics
Zeroth law: if body A is in thermal equilibrium with body C, and body B is also in thermal equilibrium with C, then A and B are in thermal equilibrium with each other.
It sounds obvious, but it is very important. It tells us that there is a quantity that is equal for all bodies in equilibrium. That quantity is temperature. So the zeroth law gives a proper meaning to temperature.
Why is it called "zeroth"?
The first and second laws were named first. Later scientists saw that this law is more basic than both, so it was placed before the first law and called the zeroth law.
How a thermometer uses it
The thermometer is body C. When it reaches equilibrium with your body, it has your temperature. If it shows the same reading for two objects, those two objects are at the same temperature without ever touching.
State variables
A system in equilibrium is fully described by a few measurable quantities called state variables: pressure P, volume V, temperature T, amount of gas n (in moles), internal energy U and others.
A state variable depends only on the present state, not on how the system got there. (Heat and work are not state variables. They depend on the path.)
Intensive and extensive variables
- Extensive: depends on the size of the system. If you join two equal boxes of gas, it doubles. Examples: V, n, mass, U.
- Intensive: does not depend on size. It stays the same when you join two equal boxes. Examples: P, T, density.
Quick test: cut the system in half in your mind. What halves is extensive; what stays the same is intensive.
Equation of state
State variables are not all free. For a given gas, if you fix some of them, the others are fixed too. The rule that links them is the equation of state.
For an ideal gas the equation of state is
PV = nRT
where R = 8.314 J mol⁻¹ K⁻¹ is the gas constant and T is in kelvin (T = t °C + 273). Real gases follow it well at low pressure and high temperature.
Because of this rule, a state can be shown as a single point on a P–V graph. We use this idea for processes in the next lessons.
Exam tip: 1–2 mark questions often ask you to state the zeroth law, define thermal equilibrium, or sort variables into intensive and extensive.
Try it at home
Take one cup of hot water and one cup of cold water. Put a steel spoon in each for two minutes. Touch the handles (carefully). Then pour both into one steel bowl and wait five minutes. Stir and feel: the water has one single temperature in between. You made thermal equilibrium.
Key formulas and definitions
- Thermal equilibrium ⇔ T_A = T_B
- Zeroth law: A ~ C and B ~ C ⇒ A ~ B
- PV = nRT (ideal gas equation of state)
- T (K) = t (°C) + 273.15
- n = m / M (moles = mass ÷ molar mass)
- R = 8.314 J mol⁻¹ K⁻¹
Worked examples
1. A thermometer reads 36 °C when kept in water X and 36 °C when kept in water Y. Will heat flow if X and Y are mixed?
Both are in thermal equilibrium with the thermometer. By the zeroth law they are in equilibrium with each other, so they are at the same temperature. No net heat flows.
2. Sort into intensive and extensive: pressure, volume, temperature, mass, density, internal energy.
Intensive (do not depend on size): pressure, temperature, density. Extensive (depend on size): volume, mass, internal energy.
3. Convert 27 °C and −73 °C to kelvin.
T = t + 273. 27 °C → 300 K. −73 °C → 200 K.
4. Find the pressure of 2 mol of an ideal gas in a 0.05 m³ vessel at 300 K. (R = 8.31 J mol⁻¹ K⁻¹)
P = nRT / V = (2 × 8.31 × 300) / 0.05 = 4986 / 0.05 = 99 720 Pa ≈ 1.0 × 10⁵ Pa (about 1 atm).
5. A gas at 300 K is heated at constant pressure until its volume doubles. What is the new temperature?
At constant P and n, V ∝ T. V doubles, so T doubles: T = 2 × 300 = 600 K (327 °C).
6. A tyre holds air at 2.0 × 10⁵ Pa at 27 °C. After a long drive the air is at 57 °C. The volume stays the same. Find the new pressure.
At constant V and n, P ∝ T (in kelvin). T₁ = 300 K, T₂ = 330 K. P₂ = P₁ × T₂/T₁ = 2.0 × 10⁵ × 330/300 = 2.2 × 10⁵ Pa.
Common mistakes
- Saying bodies in equilibrium have the same heat. They have the same temperature; the heat stored can be very different.
- Using °C in PV = nRT. Always change to kelvin first.
- Calling heat or work a state variable. They depend on the path taken, so they are not.
- Thinking equilibrium means molecules stop moving. Molecules keep moving; only the average (big) quantities stop changing.