The heat Q needed to increase the temperature of a sample with mass m and specific heat c by an amount ΔT is:
[tex]Q=mc\Delta T[/tex]On the other hand, a change in temperature in Farenheit is related to a change in temperature in Celsius as:
[tex]\Delta T_C=\frac{5ºC}{9ºF}\Delta T_F[/tex]Replace m=7.3kg, c=385J/(kgºC), as well as the final and initial temperatures to find the heat required to raise the temperature of the sample of Copper:
[tex]Q=(7.3\operatorname{kg})(385\frac{J}{\operatorname{kg}ºC})(865ºF-38ºF)[/tex]Since the specific heat is given in units of Joules per kilogram per degree Celsius, introduce the factor 5ºC/9ºF to write the change in temperature in degrees Celsius:
[tex]\begin{gathered} Q=(7.3\operatorname{kg})(385\frac{J}{\operatorname{kg}ºC})(865ºF-38ºF)\times\frac{5ºC}{9ºF} \\ =1,291,268.611\ldots J \\ \approx1.3\times10^6J \end{gathered}[/tex]Therefore, the amount of heat required to raise the temperature of the 7.3 kg of Copper sample from 38ºF to 865ºF, is 1.3*10^6 Joules.