# Thermodynamics question (1 Viewer)

#### erucibon

##### Active Member
If two heated square have the same material, thickness and are in the same environment, but one has 2m^2 and one has 4m^2 surface area, what rate will each square lose energy as it becomes progressively cooler, and which will reach thermal equilibrium first?
I know that temperature difference is proportional to the rate of energy transfer, but how do i compare the energy loses bbetween the squares as they become cooler?
Thanks

#### dcosmo

##### New Member
The base equation to describe this as per the physics formula sheet - Q/t = k * A * DeltaT /d where k = thermal conductivity, A = area, DeltaT is the temperature difference between the heated material and the surrounds. So the rate of heat transferred in watts/sec (Joules) will be proportional to area.

The plate has an overall heat capacity given by Q = m * Cp * DeltaT (m = mass, Cp = specific heat of material, DeltaT as above). The larger plate will have double the mass as the smaller one as the thickness is assumed to be the same so double the heat capacity. (mass = density of material x volume = density x surface area x thickness)

Since the larger plate has double the heat capacity but loses energy at double the rate then both plates should effectively reach thermal equilibrium at the same time.