## Dissipating Heat

Wherever  current passes through a circuit or relative motion occurs in a machine, heat is generated. Sometimes this heat is useful – some of the heat produced by a car engine can be used to heat the interior of the car. Often the heat is a nuisance however, as the heat generated raises a component above it's optimum operating temperature and may damage it if it is not dissipated.

Consider a 60W filament light bulb for example, with a surface area of 120cm 2 .  When the bulb reaches a stable temperature, it produces as much energy as it loses to it's surroundings. The power loss to the surroundings is 60W/120cm 2 =0.5W/cm 2 . The bulb will remain hot for a while after it has been switched off.

The power dissipation per unit area is much larger in electronics components. Many electronic devices are packed together on silicon chips only a few millimetres or centimetres across and must dissipate up to 40 W/cm 2 . Compare this with the 100W/cm 2 of power that must be dissipated from the tiles that acted as the heat shield on the now retired space shuttle when it reenters the Earth's atmosphere. For an integrated circuit the maximum safe operating temperature is about 120 degrees Celcius. To see if the temperature of a chip is not too high, we can equate power produced to power dissipated. The heat dissipatedis proportional to the temperature difference between the chip and the ambient temperature:

Assuming thatis equal to the power P supplied to the chip (in fact it won't be since the chip does do something useful), we can write

Rearranging this equation gives

k ranges fromto. If 1 W supplied to a integrated circuit raises the temperature to 50 degrees Kelvin above ambient temperature then