   ## Measurement of the specific heat capacity of brass using a mechanical method

The method described below was proposed by Joule in 1847 and the apparatus shown in the diagram was devised by Callendar. This was originally intended to measure the mechanical equivalent of heat. This was the mechanical energy needed to produce a known amount of heat energy.

A silk band is wrapped round a brass drum (mass mB and specific heat capacity cB) with one end attached to a spring balance (S) and the other to a weight (Mg) that hangs freely. A small amount of water (mass mW) is put in the drum and the temperature of the water is measured using a bent thermometer.

The drum is rotated by hand using the wheel at the right and the spring balance reading (FS) recorded.

The frictional force between the band and the drum is:

F = Mg – FS

The couple exerted on the drum by this force is Fr where r is the radius of the drum.

If the drum makes N revolutions the work done is 2pNFr

Work done = 2pNFr = 2pNr(Mg - FS) = (mWcW + mBcB)q where q is the rise in temperature of the water and drum. (Note: This ignores the heat energy absorber by the thermometer and that lost to the surroundings).

Therefore specific heat capacity of brass (cB) = [2pNr(Mg - FS)/q - mWcW]/mB The rise in temperature should be corrected for the cooling of the apparatus during the experiment.