Advanced · 14 min
The first law of thermodynamics
Account for heat, work, and internal energy with a consistent sign convention.
Keep an energy account
The first law expresses energy conservation for a system. For a closed system with no change in overall kinetic or gravitational potential energy, write ΔU = Q − W. Here Q is heat transferred into the system, W is work done by the system on its surroundings, and ΔU is its internal energy change. Heat leaving makes Q negative; work done on the system makes W negative. Other conventions exist, so always define your signs.
Worked example
A gas receives 300 J of heat and does 120 J of work. Internal energy change = 300 − 120 = 180 J
Expansion can do work
When a gas expands against a constant external pressure, work done by the gas is W = pexternal × ΔV. An increase in volume gives positive work under this convention. In a pressure–volume diagram for a slow equilibrium process, area under the path gives the work done by the gas. Heating does not necessarily make temperature rise: some energy can leave as work. For an ideal gas, internal energy depends on temperature.
Worked example
A gas expands by 0.002 m³ against a constant external pressure of 50,000 Pa. Work done = 50,000 × 0.002 = 100 J
Check the signs
- A gas loses 80 J of heat while 120 J of work is done on it. Write Q and W using the lesson's convention and calculate ΔU.
- Compare with a gas receiving 120 J of heat while doing 80 J of work. Explain why the same internal energy change can come from different processes.