Home / Topics / Heat & Thermodynamics
First law of thermodynamics
Intermediate
Heat added equals change in internal energy plus work done.
ΔU = Q − WΔU = Q − W: heat added minus work done by the system equals the change in internal energy. It's conservation of energy.
A gas absorbs 500 J and does 200 J of work: ΔU = +300 J.
Be careful with the sign convention for work.
In more detail
The first law of thermodynamics states that the change in internal energy equals heat added minus work done by the system, ΔU = Q − W. It is energy conservation applied to thermal systems.
Real-world uses
- Engine designers apply the first law to predict work output and heat losses.
- Refrigerators are designed using energy balance from the first law.
- Car engineers use the first law to balance the heat in fuel with the work done by the piston and the energy left in the exhaust.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What sign convention is used?
Heat added is positive, and work done by the system is positive.
Can a system do work without heat?
Yes, if its internal energy decreases as it does work, as in an adiabatic expansion.
What sign convention is used for work?
Conventions differ between textbooks. Here, work done by the gas is positive, so ΔU = Q − W.
Related topics in Heat & Thermodynamics
Ideal gas equation · Avogadro's number · Internal energy · Isothermal process · Adiabatic process · Isobaric process