Efficiency of devices: Practice Questions

An electric fan consumes 80 W of electrical power. If the fan has an efficiency of 60% in converting electrical energy into useful kinetic energy of air, what is the rate at which energy is wasted as heat?

An electric motor is supplied with $$500 \text{ J}$$ of electrical energy. If it lifts a $$10 \text{ kg}$$ mass by $$2 \text{ m}$$ against gravity, what percentage of the supplied energy is wasted? (Assume acceleration due to gravity $$g = 9.8 \text{ m s}^{-2}$$)

An electric train accelerates from rest to a speed of $$20 \text{ m s}^{-1}$$. The efficiency of the electric motor in converting electrical energy to kinetic energy is $$80\%$$. If the train's mass is $$2.5 \times 10^5 \text{ kg}$$ and $$15\%$$ of the electrical energy supplied to the motor is lost as heat in the power cables before reaching the motor, what is the total electrical energy consumed from the power supply?

A small electric water pump is used to lift \(50 \text{ kg}\) of water through a vertical height of \(6 \text{ m}\) in \(20 \text{ s}\). If the electrical power input to the pump is \(250 \text{ W}\), calculate the end-use energy efficiency of the pump.
(Take \(g = 9.8 \text{ m s}^{-2}\))

A small electric motor is used to lift a weight of \(40 \text{ N}\) vertically through a distance of \(1.5 \text{ m}\) in \(5 \text{ s}\). During this process, the motor draws a constant current of \(0.5 \text{ A}\) from a \(30 \text{ V}\) DC power supply. What is the end-use energy efficiency of the motor?

State the primary energy conversion that occurs in a gas discharge lamp during its operation, and explain why it is generally considered more efficient than an incandescent lamp.

An incandescent bulb has a luminous efficacy of $$12\text{ lm/W}$$. A new LED bulb provides the same luminous flux of $$720\text{ lm}$$ but consumes only $$9\text{ W}$$ of power. What is the luminous efficacy of the LED bulb?

A new LED street light has a luminous efficacy of $$120 \text{ lumens/W}$$, while an old sodium lamp has $$80 \text{ lumens/W}$$. If both produce a luminous flux of $$6000 \text{ lumens}$$, what is the difference in electrical power consumed between the two lamps?

A factory uses an electric motor to power a conveyor belt. The motor has an efficiency of $$85\%$$ and the conveyor belt system has an efficiency of $$70\%$$ in converting mechanical energy from the motor into useful work. If the conveyor belt is lifting $$500 \text{ kg}$$ of material by $$10 \text{ m}$$ in $$30$$ seconds, calculate the total electrical power consumed by the motor. (Assume acceleration due to gravity $$g = 9.8 \text{ m s}^{-2}$$)

A power plant uses coal to generate electricity. It has a thermal efficiency of $$40\%$$ in converting coal's chemical energy into electrical energy. The electricity is then transmitted through power lines with an efficiency of $$95\%$$. Finally, a household electric heater connected to the grid has an efficiency of $$98\%$$ in converting electrical energy into heat.

(a) Calculate the overall efficiency of energy conversion from the chemical energy in coal to the heat produced by the electric heater.

(b) If the heater produces $$2.0 \text{ MJ}$$ of useful heat, what mass of coal (calorific value $$25 \text{ MJ kg}^{-1}$$) was originally consumed at the power plant?

(c) Briefly discuss one major factor that limits the efficiency of a thermal power plant, even with advanced technology.