The temperature and density dependences of the electronic specific heat

The specific heat of an electron fluid is determined for low but nonzero temperature and for high density based on the first- and second-order exchange graphs and the ring diagrams. The specific heat constant γ is found to increase at lower temperatures for r_s of order 2 or 3. The specific-heat effective mass determined by experiments should increase accordingly. For very small r_s the specific heat is below the ideal-gas value. For r_s = 2, the deviation from a straight line of the specific-heat curve plotted against temperature is expected to start at around 2 K and increases at low temperatures. The temperature dependence is characterized by logarithmic terms.