Physic Labs

Thermal physics

Internal energy and its change

Vary heat input and compressive work on a gas model and verify the first law ΔU=Q+Won\Delta U=Q+W_{\mathrm{on}}: every joule delivered as heat or as work on the system appears as internal energy.

High school

Equipment

  • Virtual gas container with randomly moving particles
  • Sliders “Nhiệt nhận Q” (heat in), “Công lên hệ W” (work on system), “Nhiệt độ ban đầu” (initial temperature)
  • Energy-balance readout and particle-speed view

Procedure

  1. Add heat only

    Set the work slider W to zero and raise the heat input Q. The particles speed up and the readout grows: with W=0, all of Q becomes internal energy, ΔU=Q\Delta U=Q. Read ΔU\Delta U and the implied temperature change.

  2. Add work only

    Return Q to zero and raise the work slider — the model's piston does work on the gas. Check that the same energy increase results: ΔU=Won\Delta U=W_{\mathrm{on}}. Compare the particle speeds with the pure-heating case at equal ΔU\Delta U.

  3. Combine heat and work

    Set both Q and W to positive values, note their sum, and check ΔU=Q+Won\Delta U=Q+W_{\mathrm{on}} on the readout. Then pick a target ΔU\Delta U and find two different (Q, W) pairs that reach it — energy is a state function, indifferent to the path.

  4. Vary the starting point

    Change the initial-temperature slider and repeat one transfer. The same Q or W produces the same ΔU\Delta U regardless of the starting temperature — evidence that heat and work are modes of transfer, not properties of the gas.

Simulation

Experiment history

Benjamin Thompson (Count Rumford) showed in 1798 that boring cannon generates heat without limit, casting doubt on the caloric theory that treated heat as a conserved fluid. James Prescott Joule's paddle-wheel measurements of the 1840s then gave the equivalence precise numbers: about 772 foot-pounds of work per British thermal unit. Rudolf Clausius's 1850 memoir turned this into the first law of thermodynamics, ΔU=Q+W\Delta U=Q+W, with internal energy defined as a state function — heat and work being only ways to move energy across a boundary. William Thomson (later Lord Kelvin) championed the formulation, which became the foundation of all heat engines, refrigerators and chemical energetics.

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