Question

What is a perpetual motion machine? Can such a machine exist given the laws of thermodynamics?

Short answer

A perpetual motion machine is a hypothetical machine that operates indefinitely without energy input, which is impossible due to the first law of thermodynamics (energy conservation) and the second law (entropy increase).

Step-by-step solution

Define Perpetual Motion Machines

A perpetual motion machine is a hypothetical machine that can do work indefinitely without an energy source. This kind of machine is impossible, as it would violate the first or second law of thermodynamics.

Apply the First Law of Thermodynamics

The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed in an isolated system. Therefore, a machine that runs indefinitely without energy input is not possible.

Apply the Second Law of Thermodynamics

The second law of thermodynamics states that the entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value. Thus, no machine can be perfectly efficient and perpetually moving without increasing entropy or losing energy to its surroundings.

Key concepts

First Law of Thermodynamics

The first law of thermodynamics, also known as the law of energy conservation, is a foundational principle in physics that influences our understanding of energy systems. It asserts that within an isolated system, energy can neither be created nor destroyed; it can only change forms. For example, electrical energy can be transformed into mechanical energy in a motor.

This law is at odds with the notion of a perpetual motion machine. Such a device, functioning indefinitely without any external energy input, would effectively create energy out of nothing, violating this fundamental law. In practical terms, if you had a ball rolling without friction, it would move forever. Yet, in reality, energy losses like friction make perpetual motion impossible, reinforcing the first law of thermodynamics.

Second Law of Thermodynamics

The second law of thermodynamics addresses the direction of physical processes and the concept of entropy. It states that in any natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems will increase. Entropy can be thought of as the measure of disorder or randomness in a system, or the energy not available for work.

Applying this to perpetual motion machines, they would require a 100% conversion of energy from one form to another without any loss—an impossibility, as some energy will always become unusable, typically as heat. This law provides a fundamental explanation for why energy eventually spreads out and why a perpetual motion machine, which would need to maintain order and fully convertible energy, cannot exist in our universe.

Energy Conservation

Energy conservation is a concept inherent to the first law of thermodynamics and is key to understanding why perpetual motion machines are unfeasible. It holds that energy in a system must be accounted for. In any machine, energy is conserved by transforming it from one form to another—like chemical energy in fuel to kinetic energy in a vehicle. However, in every transformation, some energy is inevitably lost as heat or other less useful forms.

For a perpetual motion machine to work, it would have to ensure that no energy escapes the system and its internal mechanisms, which defies our empirical knowledge of energy interactions. Reality shows us that energy leaks and dissipation are natural and inevitable, thus conserving energy in a closed loop without any loss forever is not realistic.

Entropy

Entropy represents disorder within a system and is central to the second law of thermodynamics. It's a measure of the number of specific ways a thermodynamic system can be arranged, commonly understood as the state of randomness or chaos. As processes occur, they tend to move from a state of order (low entropy) to a state of disorder (high entropy), such as ice melting into water.

In terms of a perpetual motion machine, entropy presents a barrier. To function perpetually, the machine would need to maintain or decrease its entropy. However, the natural tendency of entropy is to increase, which necessitates energy input to compensate for this increase—thus contradicting the concept of a machine that operates without external energy. Entropy ensures that systems move towards equilibrium—where the energy is evenly distributed and no work can be extracted from the system, spelling doom for the idea of perpetual motion.