Maxwell's thermodynamic relations
Thermodynamic potentials (UG) · Physics
Gas piston lab
Interactive 3DHeat the gas and watch molecules speed up — pressure obeys the gas laws live.
Controls
Drag the sliders or type a value — the simulation updates live.
K
200K600K
×
0.5×2×
Study notes
Given: A gas with specific heat at constant pressure Cp and constant volume Cv. We want to find the relation between (dP/dT)_V and (dS/dV)_T. Using Maxwell relation: (dS/dV)_T = (dP/dT)_V. For an ideal gas, P = nRT/V. Differentiating P with respect to T at constant V gives dP/dT = nR/V. Therefore, (dS/dV)_T = nR/V. This shows how entropy changes with volume at constant temperature is directly linked to pressure and temperature gradients.