# Rate of heat flow

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The rate of heat flow between two systems is measured in watts (joules per second). The formula for the rate of heat flow is

${\displaystyle {\frac {\Delta Q}{\Delta t}}=-KA{\frac {\Delta T}{x}},}$

where ${\displaystyle {\frac {\Delta Q}{\Delta t}}}$ is the rate of heat flow, ${\displaystyle -K}$ is the thermal conductivity factor, ${\displaystyle A}$ is the surface area, ${\displaystyle \Delta T}$ is the change in temperature, and ${\displaystyle x}$ is the thickness of the material (${\displaystyle {\frac {\Delta T}{x}}}$ is called the temperature gradient and is always negative because the heat always flows from the higher temperature to the lower).

## Example

Assume there are two systems with the same mass and specific heat. System A has an average temperature of 500 kelvins, and system B has an average temperature of 400 K. If 30 seconds after the systems are put in contact they both reach 450 K, then the average rate of heat flow is

50 J/(30 s) ≈ 1.67 W.

(note: specific heat capacities = 1 J/(kg K) and masses = 1 kg).