Revision summary

Choose the system, identify whether energy crosses its boundary as heating or work, then decide whether its temperature, phase or both change.

State quantities and process transfers

Internal energy U is associated with microscopic kinetic and potential energies. It excludes the whole system's bulk kinetic and external gravitational potential energies. At equilibrium the macroscopic state determines U, so ΔU between the same endpoints is independent of the route. Q and W describe transfers during a process and can depend on that route.

Thermodynamic temperature relates to mean microscopic kinetic energy in the classical model. For an ideal gas, mean translational energy is 3kT/2. Only for the stated monatomic ideal-gas model may its full internal energy here be written:

Equal temperature does not imply equal total U. Net heating is from hotter to colder; thermal equilibrium has no net heating. By the zeroth law, if A and B each equilibrate with C, then A and B are in equilibrium with each other.

Keep the work convention visible

Heating into the system makes Q positive. Expansion makes W_on negative; compression makes it positive. In the supplied expansion, 450 J enters by heating, 180 J leaves as work and U increases by 270 J.

Use absolute external pressure. A slow frictionless process permits the gas-pressure p-V area interpretation. Insulation means Q = 0, not necessarily ΔU = 0. A rigid boundary removes volume work but does not exclude all possible work transfers. Expansion into zero external pressure has no displacement work.

Select the thermal equation by stage

Specific heat capacity is heating required per unit mass per unit temperature rise under stated conditions. Specific latent heat is heating required per unit mass for the specified phase change at constant temperature under stated pressure and conditions. Use compatible mass units and the appropriate property value.

For 0.0800 kg ice at -5.0°C becoming water at 25.0°C, the supplied stages require 840 + 26720 + 8400 = 35960 J. A horizontal temperature segment can have continuing energy input. An energy-axis graph does not directly give a time duration.

If energy is insufficient for a full phase change, calculate the mass changed using Q/l before attempting a temperature rise. If volume work is appreciable, use the first law too: the separate vaporisation example has Q = 18000 J but ΔU = 16800 J after 1200 J work output.

Check a measurement's energy destinations

A heater-and-sample assembly receives electrical work; the sample alone may receive heating from that heater. Do not count the same input twice. In the corrected calorimetry example:

Apparatus warming uses its actual endpoint temperature change; heat-loss corrections need independent evidence under comparable conditions. Assigning all input to the sample gives too high a c in this model.

The fusion comparison uses 5010 J for an extra 15.00 g melted, giving l_f = 3.34 × 10⁵ J/kg. It requires matched background transfer, correct initial thermal conditions and complete collection. The draining vessel alone is not a closed fixed-mass system.

Quantities and units

An unqualified W in the plus-sign first law means work on the system. The unit W in a power value means watt. Likewise, specific heat capacity c here is not the microscopic speed c used in a kinetic-gas derivation.