Perpetual motion. A machine that could in principle operate...

Perpetual motion. A machine that could in principle operate for ever, in spite of the presence of friction or exhaust heat, is said to be capable of 'perpetual motion', and is called a perpetuum mobile from the Latin. This concept no longer features much in the study of thermal physics, but it played a useful role historically in getting clarity about what processes are and are not possible. Two types of perpetuum mobile may be distinguished. A perpetual motion machine of the first kind produces more energy that it uses. A perpetual motion of the second kind produces exactly as much energy as it uses, and keeps running indefinitely by recycling all the output energy, whether it is produced in the form of work or heat. (i) Explain which of the laws of thermodynamics are broken by such machines. (ii) Show how a perpetuum mobile of the second kind could be constructed by combining two reversible heat engines of different efficiencies (if they could be found).

Perpetual motion. A machine that could in principle operate for ever, in spite of the presence of friction or exhaust heat, is said to be capable of 'perpetual motion', and is called a perpetuum mobile from the Latin. This concept no longer features much in the study of thermal physics, but it played a useful role historically in getting clarity about what processes are and are not possible. Two types of perpetuum mobile may be distinguished. A perpetual motion machine of the first kind produces more energy that it uses. A perpetual motion of the second kind produces exactly as much energy as it uses, and keeps running indefinitely by recycling all the output energy, whether it is produced in the form of work or heat.
(i) Explain which of the laws of thermodynamics are broken by such machines. (ii) Show how a perpetuum mobile of the second kind could be constructed by combining two reversible heat engines of different efficiencies (if they could be found).

Key Concepts

Perpetual Motion Machines

This concept refers to hypothetical devices that would operate indefinitely without any external energy input. They are typically categorized into different types based on whether they violate energy conservation or the second law of thermodynamics. While such machines have no basis in real physics because they attempt to defy fundamental natural laws, they serve as useful thought experiments for understanding the limitations imposed by these laws in physics.

First Law of Thermodynamics

The first law of thermodynamics is essentially the law of energy conservation, stating that energy cannot be created or destroyed, only transformed from one form to another. A machine that produces more energy than it uses would violate this principle, making its operation physically impossible. This law is the cornerstone of energy balance in all physical systems.

Second Law of Thermodynamics

The second law of thermodynamics deals with the direction of energy transformations and introduces the concept of entropy, which is a measure of disorder. It implies that some energy will always be lost as waste heat in any energy conversion process, and no machine can be 100% efficient. A perpetual motion machine of the second kind, which claims to recycle all its energy without losses, violates this law by neglecting the inevitable increase in entropy.

Reversible Heat Engines

Reversible heat engines are idealized systems that operate in a way that the processes can be reversed without leaving any net change in either the engine or its surroundings. They serve as theoretical models because they achieve the maximum possible efficiency given by the Carnot efficiency. The concept is central to understanding why real engines, which inevitably involve irreversibilities, cannot attain such perfection and why proposals for perpetual motion fail.

Heat Engine Efficiency

Heat engine efficiency is defined as the ratio of useful work output to the energy input from heat. It is fundamentally limited by the temperatures of the working substance’s hot and cold reservoirs, as expressed by the Carnot efficiency limit. This concept highlights that any real engine must convert some portion of the input energy into waste heat, preventing the possibility of a machine that continuously cycles energy without losses.

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