§ 16.1 Internal energy
Key ideas
- Internal energy is the sum of the random kinetic and potential energies of all the molecules.
- It depends only on the state of the system (and for an ideal gas, only on temperature, since there are no intermolecular forces).
- A rise in temperature means a rise in the average molecular kinetic energy, hence in internal energy.
Watch out: for an ideal gas, internal energy depends on temperature alone. An isothermal change (constant T) has ΔU = 0 even though the gas may be compressed and heated at the same time.
§ 16.2 The first law of thermodynamics
Key ideas
- When a gas expands at constant pressure it does work on its surroundings; when compressed, work is done on it.
- The first law is energy conservation: the rise in internal energy equals the heat added to the gas plus the work done on it.
- Sign convention: q is the heat supplied to the gas, W is the work done on the gas. Compression gives positive W; expansion negative.
Equations
W = p ΔVwork at constant pressure (magnitude)J
ΔU = q + Wfirst law: q heat in, W work done on the gasJ
Fig. 1 · The first law in a cylinder: heat q entering and work W done on the gas both raise its internal energy; here the gas instead expands, doing work on the piston.
Watch out: keep the signs straight. When a gas expands, it does work on the surroundings, so the work done on the gas W is negative; an expanding gas with no heat flow cools.