Physic Labs

Classical statistical mechanics

Internal energy and enthalpy

Compare internal energy U and enthalpy H=U+pVH=U+pV as temperature and a control parameter vary, and connect the difference to the heat capacities CV=(∂U/∂T)VC_V=(\partial U/\partial T)_V and Cp=(∂H/∂T)pC_p=(\partial H/\partial T)_p.

Undergraduate

Equipment

  • Two canvases: 3D qualitative model and normalized quantitative plot of U, pV and H
  • Slider “Nhiệt độ” (temperature)
  • Slider “Tham số” (control parameter)

Procedure

  1. Track U and H with temperature

    Sweep the temperature slider and watch how U and H=U+pVH=U+pV respond on the quantitative plot. For a fixed pV term the two curves move together but stay offset by pV; read the gap and confirm it equals the pV contribution shown.

  2. Estimate the heat capacities

    Measure the slopes ΔU/ΔT\Delta U/\Delta T and ΔH/ΔT\Delta H/\Delta T from two temperature readings each. These estimate CVC_V and CpC_p; for a gas, Cp>CVC_p>C_V because at constant pressure part of the heat does expansion work.

  3. Change the control parameter

    Move the parameter slider and describe how the balance between U and the pV term changes. State which potential is natural for your constraint — U and V fixed, or H at constant p — and predict the new offset before reading it on the plot.

Simulation

Experiment history

James Prescott Joule's experiments in the 1840s showed heat and work both change a body's energy, and Rudolf Clausius organized this into the first law dU=δQ−δWdU=\delta Q-\delta W in 1850, introducing internal energy as a state function. The concept gave thermal physics the same bookkeeping rigor as mechanics. Enthalpy H=U+pVH=U+pV emerged in the 19th century for flow systems and chemistry at constant pressure, where heat exchanged equals ΔH\Delta H directly — which is why reaction heats are tabulated as enthalpies. Gibbs's thermodynamic framework then made H one corner of a family of potentials connected by Legendre transforms.

Related physicists

James Prescott JouleRudolf ClausiusWilliam Thomson (Lord Kelvin)Josiah Willard Gibbs

Related library topics

Internal energy and enthalpy