Students are designing an experiment to demonstrate the conversionof mechanical energy into thermal energy. They have designed theapparatus shown in the figure above. Small lead beads of total massM and specific heat c (heat capacity is used in Q = mc?T) fill thelower hollow sphere. The valves between the spheres and the hollowtube can be opened or closed to control the flow of the lead beads.Initially both valves are open.
a. The lower valve is closed and a student turns the apparatus 180°about a horizontal axis, so that the filled sphere is now on top.This elevates the center of mass of the lead beads by a verticaldistance h. What minimum amount of work must the student do toaccomplish this?
b. The valve is now opened and the lead beads tumble down thehollow tube into the other hollow sphere. If all of thegravitational potential energy is converted into thermal energy inthe lead beads, what is the temperature increase of the lead?
c. The values of M, h, and c for the students' apparatus are M =3.0 kg, h = 2.00 m, and c = 128 J/(kg · K). The students measurethe initial temperature of the lead beads and then conduct 100repetitions of the "elevate and drain" process. Again, assume thatall of the gravitational potential energy is converted into thermalenergy in the lead beads. Calculate the theoretical cumulativetemperature increase after the 100 repetitions.
d. Suppose that the experiment were conducted using smallerreservoirs, so that M was one tenth as large (but h was unchanged).Would your answers to parts (b) and (c) be changed? If so, in whatway, and why? If not, why not?
e. When the experiment is actually done, the temperature increaseis less than calculated in part (c). Identify a physical effectthat might account for this discrepancy and explain why it lowersthe temperature.
Students are designing an experiment to demonstrate the conversionof mechanical energy into thermal energy. They have designed theapparatus shown in the figure above. Small lead beads of total massM and specific heat c (heat capacity is used in Q = mc?T) fill thelower hollow sphere. The valves between the spheres and the hollowtube can be opened or closed to control the flow of the lead beads.Initially both valves are open.
a. The lower valve is closed and a student turns the apparatus 180°about a horizontal axis, so that the filled sphere is now on top.This elevates the center of mass of the lead beads by a verticaldistance h. What minimum amount of work must the student do toaccomplish this?
b. The valve is now opened and the lead beads tumble down thehollow tube into the other hollow sphere. If all of thegravitational potential energy is converted into thermal energy inthe lead beads, what is the temperature increase of the lead?
c. The values of M, h, and c for the students' apparatus are M =3.0 kg, h = 2.00 m, and c = 128 J/(kg · K). The students measurethe initial temperature of the lead beads and then conduct 100repetitions of the "elevate and drain" process. Again, assume thatall of the gravitational potential energy is converted into thermalenergy in the lead beads. Calculate the theoretical cumulativetemperature increase after the 100 repetitions.
d. Suppose that the experiment were conducted using smallerreservoirs, so that M was one tenth as large (but h was unchanged).Would your answers to parts (b) and (c) be changed? If so, in whatway, and why? If not, why not?
e. When the experiment is actually done, the temperature increaseis less than calculated in part (c). Identify a physical effectthat might account for this discrepancy and explain why it lowersthe temperature.
