The Mechanical Equivalent of Heat
Warming water by friction alone shows a calorie is 4.186 joules.
Lesson at a glanceShow the key points
- If work W gives the same effect as heat H: W = JH (25.3); J = 4.186 J/cal.
- Searle's cone: the spun outer cone's friction on the inner cone is balanced by Mgr; work 2πnMgr.
- J = 2πnMgr/[(m₁s₁ + m₂s₂)(θ₂ − θ₁)].
- Friction produces thermal energy directly; calling it 'heat' is traditional, not strict.
For a long time heat and work were measured in unrelated units, calories and joules. Experiments that warmed water purely by doing work proved they are the same thing and fixed the exchange rate.
The mechanical equivalent of heat
If mechanical work W produces the same temperature change as heat H:
Searle’s cone method
Two cones of the same metal fit snugly one inside the other. The outer cone A is spun on a spindle (by a motor or by hand), and a counter records its revolutions. The inner cone B, holding water, a thermometer and a stirrer, has a wooden disc of radius r on top with a cord wound round it, running over a pulley to a pan of mass M.
Friction tries to drag B round with A. Choose the direction so the hanging weight’s torque Mgr opposes the friction torque Γ, and adjust M until B stays still: Γ = Mgr. In n revolutions, the work done against friction is
All of it raises the temperature of the water (m₁, s₁) and the cones (m₂, s₂) from θ₁ to θ₂:
With r = 5.0 cm and M = 2.0 kg, the outer cone turns 500 times. The inner cone holds 200 g of water; the cones have a water equivalent of 14 g. The water warms by 3.44°C. Find J.
- 1W = JH; J = 4.186 J/cal.
- 2Searle's cone: friction work 2πnMgr, balanced so the inner cone is still, warms water and cones.
- 3J = 2πnMgr/[(m₁s₁ + m₂s₂)(θ₂ − θ₁)].
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