Joule's Paddle Wheel — Where Lost Energy Goes
Where does energy go when it seems to disappear — when two cars crash and crumple, or when a falling weight lands without bouncing? In the 1840s James Prescott Joule answered with falling weights, paddles and a thermometer. This is a bench copy of his idea: two lead weights hang from cords wound on a drum, and as they fall the drum turns a spindle carrying four tiers of brass paddles inside an insulated copper vessel of water, shown in cutaway. Fixed vanes on the vessel wall stop the water from simply swirling round, so the paddles churn it. Press play and the weights fall 20 times, wound back up between falls, while a close-up shows the inside of the vessel, the thermometer creeps up and the graph collects one point per fall.
Como usar esta simulação
- Each weight m — 2 to 20 kg, with 10 kg marked. Heavier weights do more work per fall and the temperature rise grows in proportion: after 20 falls, 0.435 K with 2 kg and 4.35 K with 20 kg.
- Fall height h — 0.50 to 2.00 m, with 1.50 m marked. The weights start at this height on the rule, and the rise is proportional to it: from 0.725 K to 2.90 K.
- Water in the vessel m_w — 0.20 to 2.00 kg, with 0.60 kg marked. More water means a larger heat capacity C and a smaller rise: 5.71 K with 0.20 kg, 0.687 K with 2.00 kg. The water level in the vessel follows the mass.
- Play/pause, back to the start, a timeline you can drag to any moment, and ½×, ¼×, ⅛× slow motion
- Drag anywhere on the scene to look around.
O que observar
- One fall: the weights sink 1.50 m at a steady 6.0 cm/s, the paddles turn 6.8 times, and the water warms by 0.109 K.
- The weights land with 0.036 J of kinetic energy out of 294 J of work: almost all of the energy went into the water.
- Winding the weights back up does not change the temperature: the paddle is unhooked from the drum, so only the falls do work on the water.
- Every fall adds the same step, so work ÷ temperature rise stays at 2704 J/K and the 20 points on the graph lie on one straight line through the origin.
- Double the weights or the height and the rise doubles; double the water and the rise falls, but not to half — the copper's 192.5 J/K stays the same.
- With less water fewer vanes are under water, so the weights sink faster — 9.9 cm/s with 0.20 kg against 3.2 cm/s with 2.00 kg — yet the rise depends only on the work and on C.
- The clock shows lab time: a fall takes 25 s and the whole run about 11 minutes, shown about ten times faster; at ⅛× a fall runs at close to its real pace.
A física por trás
Each fall, the two weights lose gravitational potential energy 2mgh = 2 × 10 × 9.8 × 1.50 = 294 J. They never speed up: the paddles' drag grows with the square of the speed, so within a few milliseconds the weights settle at a steady 6.0 cm/s, and they land with only ½ × 20 × 0.060² = 0.036 J of kinetic energy, which goes into the felt stops. Everything else, 293.96 J, is work done on the water by the paddles, and it appears as internal energy of the water and the copper, which share one temperature. Their heat capacity is C = 0.60 × 4186 + 0.50 × 385 = 2511.6 + 192.5 = 2704 J/K, so each fall warms them by 0.109 K, and the 20 falls of a run, 5880 J, take the water from 20.00 °C to 22.17 °C. The bookkeeping closes exactly: n·2mgh = CΔT + n·Eₖ. Work divided by temperature rise stays at 2704 J/K after every fall, so the points on the graph lie on one straight line through the origin with slope 1/C: twice the work, twice the rise. That is the evidence that the energy was not lost. The kinetic energy that 'disappears' when two bodies collide and stick together goes the same way — into internal energy, a slight warming of the bodies. Joule used the same reasoning to measure the mechanical equivalent of heat; the numbers here belong to this bench copy, not to his apparatus.