First law and PV work
A gas's energy changes only through heat flowing in and work being done — a checking account with exactly two transaction types.
The first law
The internal energy of a system changes by delta-U = Q - W, where Q is heat added to the system and W is work done by the system. Both signs matter: heat leaving or work done on the gas are negative entries. This is energy conservation with heat included.
\Delta U = Q - WWork and processes
At constant pressure, an expanding gas does work W = P*delta-V. Isothermal: temperature pinned, so for an ideal gas delta-U = 0 and Q = W. Adiabatic: no heat exchanged, Q = 0, so delta-U = -W. Isobaric keeps the pressure fixed; isochoric keeps the volume fixed, so no work is done.
W = P\,\Delta VWorked example
A gas at constant pressure 1.0e5 Pa expands by 2.0e-3 m^3 (2.0 liters) while absorbing 600 J of heat. The work done by the gas is W = (1.0e5)(2.0e-3) = 200 J, so the internal energy rises by delta-U = 600 - 200 = 400 J. The other 200 J of heat paid for pushing the piston.
\Delta U = Q - W = 600 - 200 = 400\ \text{J}Flashcard
First law, with work done BY the gas positive
Check your understanding
An ideal gas expands isothermally and does 150 J of work on its surroundings. How much heat flows into the gas?