Laws of Thermodynamics

Thermodynamics is an essential branch of physics that deals with the relationship between heat and other forms of energy such as mechanical, electrical or chemical energy. At its core, thermodynamics describes how different forms of energy are transferred within a closed system or between different systems. The laws of thermodynamics define these processes and set limits on how energy can be transformed and used. There are four fundamental laws of thermodynamics, often numbered from zero to three, each of which describes principles important for understanding energy interactions in physics and engineering.

Zeroth law of thermodynamics

The zeroth law of thermodynamics establishes the concept of temperature as a fundamental and measurable property of thermodynamic systems. According to this law:

If two systems are in thermal equilibrium with a third system, they will also be in thermal equilibrium with each other.

This law serves as the primary basis for the concept of temperature and its measurement. If system A is in equilibrium with system C, and system B is also in equilibrium with system C, then it means that systems A and B are in equilibrium with each other.

A ≈ C
B ≈ C
=> A ≈ B
    

For example, consider two cups of tea. If both have the same temperature as a thermometer, then they must have the same temperature as each other. The zeroth law allows the definition of a temperature scale, making it possible to measure and compare temperatures.

Example: Identifying thermal equilibrium

Imagine you have three containers filled with different substances: water, oil, and air. We use a thermometer (our third system) to measure the temperature of each. If the thermometer reads the same temperature for all three, then, according to the zeroth law, the three substances are in thermal equilibrium with each other.

First law of thermodynamics

The first law of thermodynamics is often called the law of conservation of energy. It states:

The total energy of an isolated system is constant. Energy can neither be created nor destroyed but it can only be converted from one form to another.

In mathematical expression this can be written as:

ΔU = Q – W
    

• ΔU is the change in the internal energy of the system.
• Q is the heat added to the system.
• W is the work done by the system on its surroundings.

The first law implies that any increase in the internal energy of a system is a result of heat added to the system or work done on the system.

Example: Heating and expansion of a gas

Consider a piston filled with gas. When the gas is heated, it expands, pushing the piston outward. Here:

• The added heat (Q) causes the gas molecules to move faster, increasing the internal energy (ΔU).
• This system does work (W) on the surroundings by pushing the piston outward.

In this scenario, if you measured the amount of heat added Q and the work done W, you can determine the change in the internal energy ΔU of the gas using the first law.

Second law of thermodynamics

The second law of thermodynamics introduces the concept of entropy, which is often interpreted as a measure of disorder or randomness in a system. This law states:

The total entropy of an isolated system can never decrease with time. It can remain constant for reversible processes but increases for irreversible processes.

In short, this law implies that natural processes tend towards a state of maximum disorder or entropy. This has profound implications for the direction of heat transfer and the efficiency of engines.

Heat engines and efficiency

Consider a heat engine operating between two reservoirs: a hot reservoir and a cold reservoir. According to the second law, the engine can never convert all the heat (Q_h) absorbed from the hot reservoir into work (W). Some energy inevitably goes to the cold reservoir as waste heat (Q_c).

η = 1 - (Q_c / Q_h)
    

• η is the efficiency of the heat engine.
• Q_c is the heat expelled into the cold storage.
• Q_h is the heat absorbed from the hot store.

No engine operating between two heat reservoirs can be more efficient than the Carnot engine, which operates in a completely reversible manner.

Example: Entropy in the real world

Imagine you have a cup of hot coffee left at room temperature. Over time, the coffee cools as heat flows from the coffee into the air. This process is irreversible, meaning you cannot return the heat from the air to the coffee naturally without external work. This process involves an increase in entropy, as more of the energy is dispersed into the environment.

Third law of thermodynamics

The third law of thermodynamics refers to the properties of systems at absolute zero temperature. It states:

As the temperature of a system approaches absolute zero, the entropy of a perfect crystalline structure approaches zero.

This law implies that it is impossible to reach absolute zero by any finite number of processes and all processes in a system cease at absolute zero because entropy is minimum and all molecular motion stops. Absolute zero is theoretically the lowest possible temperature, where the thermal energy of the system is minimum.

Example: Cooling to near absolute zero

Research labs use various methods such as laser cooling and dilution refrigeration to reach temperatures just a degree above absolute zero. While true absolute zero is impossible to achieve, scientists can approximate it very closely and observe unique quantum mechanical effects.

Understanding these fundamental laws of thermodynamics is crucial for explaining and predicting how energy systems behave. These concepts open up a wide range of applications, from power generation and refrigeration to understanding the ultimate fate of the universe.

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