Question

The electrical power supplied to the motor is much greater than the answer to (b).Explain how the principle of conservation of energy applies to this system.

Answer 1

The principle of conservation of energy states that energy in an isolated system is constant and can only change forms, not be created or destroyed. In an electric motor, power supplied is greater than the mechanical output due to energy losses, which aligns with energy conservation. Similarly, a heat pump moving heat from one place to another can have greater energy output than input without violating the first law of thermodynamics.

The student's question is about the relationship between the electrical power supplied to a motor and the principle of conservation of energy. According to the conservation of energy, the total energy in an isolated system remains constant, meaning that energy can neither be created nor destroyed, only transformed from one form to another. In the context of an electric motor, the electrical power supplied is greater than the mechanical power output due to energy losses through mechanisms such as heat, sound, and friction. This energy has not disappeared but has been converted into forms that do not contribute to the mechanical work done by the motor.

When discussing constants and powers in parallel connections, we must realize that they are indeed greater than in series connections. This is consistent with the conservation of energy since the principle dictates that the total energy input will equal the total sum of energy outputs and losses. For instance, if the electrical power supplied (Pm) is 1.6 × 10³ W, and the resistive loads (Pr) and source power (Ps) are 8.0 × 10² W and 2.4 × 10³ W respectively, we have an energy balance where the supplied power is converted into useful work and lost energy (like heat).

The example of a heat pump producing more energy than it consumes is also consistent with conservation of energy. The first law of thermodynamics, which is a statement of energy conservation, is not violated because the heat pump is moving heat from one place to another rather than creating energy. It operates like a refrigerator, transferring thermal energy against the natural flow from cold to hot, which is why the output energy can be greater than the input energy.

Answer 2

The principle of conservation of energy states that energy cannot be created or destroyed; it can only be converted from one form to another or transferred between objects. In the case of the motor system mentioned this principle applies as well.

The electrical power supplied to the motor is converted into mechanical power to rotate the motor. However due to losses such as friction and heat not all of the electrical power is converted into mechanical power. Some energy is lost in the form of heat sound or other forms of dissipation.

So although the electrical power supplied to the motor may be greater than the mechanical power output (answer to (b this does not violate the conservation of energy principle. The total energy input (electrical power) is still conserved in the system but some of it is transformed into other forms of energy that are not accounted for in the mechanical power output.

In other words the excess electrical power not converted into mechanical power is dissipated as waste energy resulting in a lower mechanical power output. This is a result of the inherent inefficiencies and losses in the system. The conservation of energy principle ensures that the total energy remains constant despite the conversion and dissipation of energy within the system.