What is the specific heat of liquid copper? All I know is that the specific heat of the solid copper is 390 J/kg*C
That sounds right. Due to matalic bonds being to say the least a bit odd from a chemistry and quantum mechanics point of view metal atoms can vibrate more freely than you would expect from common sense. So all metals have a specific heat capacity that to me is surprisingly low. Also compare that to the 4200j/kgC for water which only weighs 1kg/litre! Strange but true
The enthalpy of liquid copper up to a temperature of 2000 K is investigated by the drop method with an error from 1 to 1.5%. The measurement results are compared with the literature data. It is shown that the spectral emissivity of copper melt depends on temperature. The obtained data on enthalpy are approximated by an equation. The true heat capacity of liquid copperc p = 36.33 J/(mol K), the melting heat ΔH = 13.59 kJ/mol, and the melting entropy ΔS = 10.0 J/(mol K) of copper are calculated.