Daily Physicist

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Today is the birthday of

• Valentine Telegdi (1922-2006).

Today’s Problem: Heat absorbed in an isothermal expansion

Using the ideal gas law, \(PV=NkT\), and the fact that the internal energy of an ideal gas depends only on the temperature, find the amount of heat absorbed in an isothermal expansion.

Answer

Since the temperature remains constant there is no change in internal energy. By the first law of thermodynamics this means the heat absorbed must equal the amount of work done by the gas, \(Q=W\). The work done by the gas is given by

\[W = \int_{A}^{B}P\,dV = NkT\int_{A}^{B}\,dV/V = NkT\ln(V_B/V_A)\]

Note that for an expansion \(V_B\gt V_A\), \(Q\) is positive and heat is absorbed. For a contraction, \(V_B\lt V_A\), \(Q\) is negative and heat is dissipated.