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The First Law of Thermodynamics. Heat Capacity

  • The first law of thermodynamics:
    $$Q = \Delta U + A,$$

    where $ \Delta U $ is the increment of the internal energy of the system.

  • Work performed by gas:
    $$A = \int pdV.$$
  • Internal energy of an ideal gas:
    $$ U = \frac{m}{M}C_V T = \frac{m}{M} \frac{RT}{\gamma - 1} = \frac{pV}{\gamma - 1}.$$
  • Molar heat capacity in a polytropic process ($\displaystyle pV^n = const $):
    $$ C = \frac{R}{\gamma -1} - \frac{R}{n-1} = \frac{(n-\gamma)R}{(n-1)(\gamma-1)}.$$
  • Internal energy of one mole of a Van der Waals gas:
    $$U = C_V T - \frac{a}{V_M}.$$
Keywords: 
first law, internal energy, molar heat capacity, polytropic
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