How do you get from energy q equals mCAT to energy density?

Answer 1

To get from the equation for energy, ( q = m \cdot C \cdot \Delta T ) (where ( q ) is energy, ( m ) is mass, ( C ) is specific heat capacity, and ( \Delta T ) is the change in temperature) to energy density, you divide the total energy ( q ) by the volume ( V ) of the material. This gives you energy density ( u ) as ( u = \frac{q}{V} = \frac{m \cdot C \cdot \Delta T}{V} ). Since mass ( m ) can also be expressed as density ( \rho ) multiplied by volume ( V ) (i.e., ( m = \rho \cdot V )), you can substitute to obtain: ( u = \rho \cdot C \cdot \Delta T ).