Companion to the reading passage The Weight of Heat: A Honeymoon, a Waterfall, and the Law That Changed Physics. Answer each question, then click Check. Multiple-choice and number questions grade themselves; for written answers, compare yours with the model answer and checklist, then score yourself honestly.
In the 1840s, James Prescott Joule showed that stirring water makes it warmer by an amount that depends on the work done on it. A group of students built a modern version of his apparatus, described in Model 1.
Model 1: A 20.0-kilogram mass hangs from a cord that runs over a pulley and wraps around the axle of a paddlewheel. The paddlewheel sits inside an insulated container holding 0.500 kilogram of water. When the mass is released, it falls a vertical distance of 1.50 meters at a slow, nearly constant speed, and the cord spins the paddles, which stir the water. The students then lift the mass back up and repeat the drop.
1. Substitute numerical values into a mathematical representation that can be used to determine the decrease in gravitational potential energy of the Earth–mass system during one drop of the mass. Then calculate the decrease. (Use g = 9.8 m/s2.)
The students recorded the total temperature rise of the water after different numbers of drops. Table 1 shows their results. The specific heat of water is 4.18 × 103 J/(kg•°C).
Data are representative values for practice.
Table 1: Temperature Rise of the Water
| Number of Drops | Total Distance Fallen by the Mass (m) | Temperature Rise of the Water (°C) |
|---|---|---|
| 5 | 7.50 | 0.66 |
| 10 | 15.0 | 1.32 |
| 15 | 22.5 | 1.98 |
| 20 | 30.0 | 2.64 |
2. Which graph best represents the relationship between the temperature rise of the water and the total distance fallen by the mass?
3. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
Joule reasoned that water falling down a tall waterfall should be slightly warmer at the bottom than at the top. In 1847 he and William Thomson tried to measure this at a waterfall in the French Alps with a fall of about 268 meters. Spray filled the air, wind broke the falling water into many separate streams, and they could not get a reliable reading.
Consider the Earth–water system for a small parcel of water that starts at rest at the top of the waterfall (Position A). Position B is halfway down the fall. Position C is after the parcel has landed and come to rest in the pool at the bottom. The pool is the zero level for gravitational potential energy.
4. A prediction that all of the water’s gravitational potential energy becomes internal energy of that same water gives a temperature rise of about 0.6 °C. Which statement best explains why the actual temperature rise at the waterfall would likely be less than this prediction?
5. The energy bar graph for the Earth–water system at Position A is PEg = ET, KE = 0, Eother = 0. Construct the energy bar graph for the Earth–water system at Position B (halfway down the fall). The pool is the zero level for PEg. Assume air resistance is negligible while the water is falling.
Click a box to set each bar’s height; click it again to clear the bar to 0. The ET bar is drawn for you.
6. Construct the energy bar graph for the Earth–water system at Position C (after the parcel has landed and come to rest in the pool). The pool is the zero level for PEg.
Click a box to set each bar’s height; click it again to clear the bar to 0. The ET bar is drawn for you.