Question

An inventor claims to have developed a resistance heater that supplies \(1.2 \mathrm{kWh}\) of energy to a room for each kWh of electricity it consumes. Is this a reasonable claim, or has the inventor developed a perpetual-motion machine? Explain.

Short answer

Explain your answer. Answer: Yes, the inventor's claim violates the Law of Conservation of Energy because it suggests that the device would be more than 100% efficient, which is impossible. According to the conservation laws, the total energy input must be equal to the total energy output within a closed system, and energy can only be converted from one form to another, not created or destroyed. Therefore, the claim resembles a perpetual-motion machine, which is considered scientifically and theoretically impossible to create.

Step-by-step solution

Understanding the claim

The inventor claims that their resistance heater can generate 1.2 kWh of energy output for every 1 kWh of electric input. This suggests that the heater is more than 100% efficient, which means that it apparently produces more energy than it consumes.

Analyzing energy conservation

According to the Law of Conservation of Energy, the total energy in a closed system remains constant. In this case, the total energy input must be equal to the total energy output within the system. If the heater generates more energy than it consumes, it would be violating this law.

Evaluating the claim

Energy can be converted from one form to another, but it cannot be created or destroyed. In this case, it is theoretically impossible for a device to produce more energy than it consumes. The efficiency of any system cannot be greater than 100%. Therefore, the inventor's claim of supplying 1.2 kWh of energy for each kWh consumed by the heater indicates that the device would be creating energy, which violates the Law of Conservation of Energy.

Conclusion

Based on the Law of Conservation of Energy, the claim made by the inventor is not reasonable, as it suggests that the device would be more than 100% efficient, which is impossible according to the conservation laws. Hence, the inventor's claim resembles a perpetual-motion machine, which is considered scientifically and theoretically impossible to create.

Key concepts

Energy Efficiency

Energy efficiency is a measure of how well an energy conversion device, such as a resistance heater, performs in turning energy from one form, like electricity, into another form, such as heat. A critical point in evaluating energy efficiency is understanding the concept of the energy conversion ratio. This ratio is often expressed as a percentage, indicating how much input energy is converted into useful output energy. The maximum possible efficiency under the laws of physics is 100%, where all input energy is usefully converted with no losses.

• An efficiency greater than 100% would imply generating more energy than is put in, which contradicts the Law of Conservation of Energy.
• Efficiency improvements usually result from reducing energy losses during conversion, like through insulation or more conductive materials.
• A 'high-efficiency' device translates to less waste and reduced energy consumption for the same output.

Therefore, a claim of a resistance heater that provides more energy than it consumes is conceptually flawed, as this would suggest an efficiency greater than 100%, which does not align with the practical realities of energy conversion.

Perpetual-Motion Machine

A perpetual-motion machine is a hypothetical device that, once started, would continue to operate indefinitely without additional energy input, thus defying the laws of thermodynamics. These machines are divided into two categories:

• Perpetual motion of the first kind: they produce work without energy input, violating the Law of Conservation of Energy.
• Perpetual motion of the second kind: they spontaneously convert heat energy into mechanical work, contrary to the second law of thermodynamics that states entropy within an isolated system cannot decrease.

The idea of a resistance heater supplying more heat energy than the electrical energy consumed aligns with the concept of a perpetual-motion machine of the first kind. Such a device would continually produce excess energy from nothing, which is not scientifically feasible due to the aforementioned laws. The inventor's claim is, thus, a classic example of an attempt to propose a perpetual-motion machine, which is impossible to achieve in reality.

Thermodynamics

Thermodynamics is a branch of physics that deals with heat, work, temperature, and the statistical behavior of systems with respect to these quantities. It's grounded in four fundamental laws:

• The zeroth law establishes thermal equilibrium and the basis for temperature.
• The first law, often synonymous with the Law of Conservation of Energy, asserts that energy cannot be created or destroyed in an isolated system.
• The second law introduces the concept of entropy, a measure of the disorder in a system, stating that entropy tends to increase over time in an isolated system.
• The third law dictates that a system's entropy approaches a constant value as the temperature approaches absolute zero.

In the context of the resistance heater claim, thermodynamics signifies that the electrical energy converted into heat must be equivalent to or less than the electrical energy input, corroborating that the notion of generating more heat than the electrical energy provided defies the first law of thermodynamics. As such, the solution provided in the textbook applies these fundamental principles to judge the validity of the inventor's claim.

Resistance Heater

A resistance heater is a common device used to convert electrical energy into thermal energy for the purpose of heating. The electric current passes through a resistor, typically a wire or coil, heating it up due to its inherent electrical resistance. The heat is then transferred to the surrounding environment, usually air or water. Key points regarding resistance heaters include:

• The efficiency of resistance heaters is generally high, with almost all of the electric energy converted into heat.
• Energy losses in these heaters occur primarily through thermal conduction, convection, and radiation to non-target areas.
• Even with high efficiency, no resistance heater can create more heat energy than the electrical energy it uses, which is why a claim of a heater performing at over 100% efficiency suggests a fundamental misconception.

In modern practice, resistance heaters are designed to maximize energy transfer to the desired area, but none can circumvent the Law of Conservation of Energy, rendering any claim that suggests such capability scientifically baseless.