能量守恆與耗散：練習題

Energy can be transferred usefully, stored, or dissipated. In a closed system, what happens to the total energy during an energy transfer?

A student uses an electric motor to lift a weight. The motor has a total power input of \(400\text{ W}\) and a useful power output of \(120\text{ W}\). Calculate the efficiency of the motor.

A system transfers \(15000\text{ J}\) of total input energy. If \(3000\text{ J}\) of this energy is dissipated as heat and sound, calculate the efficiency of the system as a percentage.

An electric motor has a total power input of 200 W. If the motor is 35% efficient, calculate the useful power output of the motor.

In a closed system, a total of \(500\text{ J}\) of energy is transferred. If \(150\text{ J}\) of this energy is dissipated to the surroundings as heat, what is the total energy remaining in the system?

State the law of conservation of energy as it applies to any energy transfer within a closed system.

Explain how the use of a lubricant on the moving parts of a motor can increase the efficiency of the machine.

A crane lifts a load of \(2000\text{ N}\) through a vertical height of \(10\text{ m}\). The total energy supplied to the crane is \(25000\text{ J}\). Calculate the efficiency of the crane and describe where the "wasted" energy is likely to have been dissipated.

A homeowner wants to reduce the rate of cooling of their house to save energy. The walls are currently made of a single layer of brick with a thermal conductivity of \(0.8\text{ W/m °C}\) and a thickness of \(0.12\text{ m}\).

(a) Explain, in terms of particles, how energy is transferred through the wall by conduction.

(b) The homeowner decides to add a layer of fiberglass insulation to the inside of the wall. The fiberglass has a thermal conductivity of \(0.04\text{ W/m °C}\) and a thickness of \(0.08\text{ m}\). Compare the effectiveness of the fiberglass insulation to the brick wall and explain how the total rate of energy transfer is affected by the thickness and thermal conductivity of these materials.

(c) Lubrication is another method used to reduce unwanted energy transfers in mechanical systems. Explain how lubrication reduces the amount of energy 'wasted' as thermal energy in a motor.