Question

(a) Over the years, there have been numerous claims about "perpetual motion machines," machines that will produce useful work with no input of energy. Explain why the first law of thermodynamics prohibits the possibility of such a machine existing. (b) Another kind of machine, sometimes called a "perpetual motion of the second kind," operates as follows. Suppose an ocean liner sails by scooping up water from the ocean and then extracting heat from the water, converting the heat to electric power to run the ship, and dumping the water back into the ocean. This process does not violate the first law of thermodynamics, for no energy is created energy from the ocean is just converted to electric energy. Show that the second law of thermodynamics prohibits the existence of such a machine.

Short answer

The first law forbids energy creation; the second law requires an increase in entropy. Both prevent perpetual motion machines.

Step-by-step solution

Understanding the First Law of Thermodynamics

The first law of thermodynamics is a restatement of the conservation of energy principle, which states that energy can neither be created nor destroyed. This means any claimed 'perpetual motion machine' that proposes to generate energy without an input or output must violate this law as it suggests energy creation from nowhere.

Application of the First Law to Perpetual Motion

A perpetual motion machine of the first kind would require a system to output energy continuously without any energy input, increasing energy in the universe. However, this contradicts the first law of thermodynamics, which requires all energy in a system to be accounted for through input, output, and internal changes.

Introduction to the Second Law of Thermodynamics

The second law of thermodynamics states that the total entropy, or disorder, of an isolated system can never decrease over time, it can only stay constant or increase. This means while energy transformations occur, they must lead to increased entropy, especially in isolated systems.

Examining the Ocean Liner Scenario

In the proposed 'perpetual motion machine of the second kind,' the liner extracts heat from ocean water, converting it into electric power without expelling any higher entropy energy byproduct. According to the second law, energy cannot be converted completely from heat to work without some waste, meaning some heat must remain or be expelled to increase entropy overall.

Violation of the Second Law by the Ocean Liner

The described machine implicitly promises 100% conversion efficiency of heat to work, which should cause a decrease in entropy, violating the second law. Instead, some energy must be released as waste heat, ensuring that entropy increases, thus making the scenario impossible.

Key concepts

First Law of Thermodynamics

The first law of thermodynamics is a fundamental principle that emphasizes energy conservation. It tells us that energy cannot be created or destroyed. Instead, it can only be converted from one form to another. This means that the total energy of an isolated system remains constant over time.
When applied to the concept of perpetual motion machines, this law becomes a barrier. Perpetual motion machines of the first kind would require an ability to produce work or energy without any energy input. In a practical sense, this would mean generating power out of nothing—an impossible feat.

• The energy balance of the universe would be disrupted if such a machine existed.
• All processes or machines that claim to have no energy input yet produce energy challenge the foundational principle of energy conservation.

Thus, according to the first law of thermodynamics, such a machine is fundamentally impossible, as it would imply energy is being created from nothing, which the law prohibits.

Second Law of Thermodynamics

The second law of thermodynamics introduces the concept of entropy, a measure of disorder or randomness in a system. This law states that in an isolated system, the total entropy can never decrease over time. Instead, it tends to increase or remain constant. This concept adds another layer of understanding to energy transformations beyond the first law.
When examining systems like the ocean liner scenario, which operate by extracting heat from water to produce work, we encounter another impossibility.

• According to the second law, converting heat entirely into work without waste leads to a decrease in entropy, which cannot happen.
• Some energy inevitably needs to be expelled or converted into non-useful energy to accommodate the increase in entropy.

Hence, the second law of thermodynamics clarifies that not all energy can be perfectly converted to work, pointing out a natural limitation on energy efficiency in systems. This excludes the possibility of a theoretical perpetual motion machine that operates by harnessing heat alone, since total conversion would defy entropy expectations.

Perpetual Motion Machines

Perpetual motion machines are fascinating in theory because they evoke the idea of endless energy output without input. However, both the first and second laws of thermodynamics robustly counter the possibility of their existence.
The first law nullifies any concept of machines creating energy from nothing, as it strictly conserves total energy.

• A machine continuously producing energy would imply energy creation, thus conflicting with the universal law of conservation.

The second law further elaborates on why 100% energy conversion from one form (like heat) directly to work, without waste, cannot occur. There is a perpetual increase in entropy.

• No machine can perfectly convert all input energy into work due to unavoidable waste energy that must be accounted for to prevent a decrease in entropy.

These physical laws delineate boundaries for energy transformation processes, making the dream of perpetual motion machines remain in the realm of fiction.