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The First Law of Thermodynamics

Thermodynamics

The first law of thermodynamics is the law of conservation of energy applied to heat and work. Energy cannot be created or destroyed, only moved or changed from one form to another.

What the first law says

The first law states that the change in a system's internal energy equals the heat added to it minus the work it does on its surroundings. Internal energy is the total kinetic and potential energy of the particles inside the system, and it depends only on the current state, such as temperature and volume. Heat and work are different ways of transferring energy across the boundary: heat flows because of a temperature difference, while work is done when a force moves something, for example when a gas expands and pushes a piston. The law applies to every process, from a kettle boiling to a car engine, and it is the bookkeeping rule that keeps energy accounts balanced.

Special cases

In a cyclic process the system returns to its starting state, so its internal energy change is zero and the net work done equals the net heat supplied. This is how an engine works: heat in, work out, and the difference rejected as waste heat. In an adiabatic process no heat flows, so any work done comes directly from the internal energy, and the temperature falls as the gas expands. In a constant-volume process no work is done, so all the heat supplied raises the internal energy and the temperature. Each of these is a special case of the same law, with one term set to zero.

Where you see it

A car engine turns only part of the fuel's chemical energy into motion; the first law says the rest must go somewhere, and it leaves as heat in the exhaust and coolant. A refrigerator uses work to move heat from cold food to warm air, and the first law accounts for both the heat removed and the work supplied. Your body is a thermodynamic system too: food supplies energy, some becomes work and body heat, and the balance is stored as fat or used for growth. No machine can produce more energy than it takes in, which is why perpetual motion machines of the first kind are impossible.

Common mistakes

• Mixing sign conventions: with delta U = Q - W, W is work done BY the system; with delta U = Q + W, W is work done ON it. Pick one and stay with it.
• Treating heat and work as stored quantities: a system has internal energy, but heat and work are transfers, not things it contains.
• Forgetting that internal energy is a state function: its change depends only on the start and end states, while heat and work depend on the path taken.

Practice questions

1. A system absorbs 800 J of heat and does 300 J of work. What is its change in internal energy?
   Show answer

   delta U = 800 - 300 = 500 J increase.

2. A gas is compressed, with 100 J of work done on it and no heat transfer. What is delta U? (Use delta U = Q - W, where W is work done by the system.)
   Show answer

   delta U = 0 - (-100) = +100 J, so internal energy rises by 100 J.

3. Why does a bicycle pump get warm when you inflate a tyre quickly?
   Show answer

   The process is adiabatic, Q = 0, so all the work done on the gas becomes internal energy and its temperature rises.

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