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A brass cylinder is rotated using a handle.  A cord wrapped around the cylinder is attached to a weight which is lifted due to the friction of the cord against the cylinder.  The friction generates heat which raises the temperature of the cylinder.  The work done can be calculated from the torque on the cylinder and the number of turns.  The heat gained can be calculated from the mass, the specific heat and the temperature rise of the brass cylinder.  Equating the two gives a value for the Mechanical Equivalent of Heat.

Mechanical equivalent of heat