Coase's first theorem

macroeconomic 748 03/07/2023 1035 Jasmine

Kelvin’s First Law of Thermodynamics The concept of thermodynamics, which explains the exchange of energy between physical systems, has been the bedrock of modern physics since the 19th century. At the centre of it is the First Law of Thermodynamics, also known as the Kelvin-Planck statement or......

Kelvin’s First Law of Thermodynamics

The concept of thermodynamics, which explains the exchange of energy between physical systems, has been the bedrock of modern physics since the 19th century. At the centre of it is the First Law of Thermodynamics, also known as the Kelvin-Planck statement or Law, which states that ‘energy can be neither created nor destroyed’. In essence, the First Law states that all energy inherently exists and is conserved; it cannot be created or destroyed, merely transferred and transformed between systems.

The First Law is usually stated in terms of an energy balance equation that says the energy lost by a dissipative system is equal to the energy gained by its surrounding environment. This is sometimes referred to as the closed system or adiabatic principle. It is the basis of most thermodynamic calculations and its mathematical form is the same as that of the second law of thermodynamics. This means that the same equations used to calculate the amount of energy that is transferred in a irreversible process, can also be used to calculate the amount of energy exchanged in a reversible process.

The first law of thermodynamics also implies that for any system to stay in equilibrium, the energy within the system must remain constant. This means that if an object is heated, the energy within the system is only transferred from one form to another (usually from chemical energy to kinetic energy) and does not change. This is useful for understanding the behaviour of conserved energy such as within a gas, which will expand as more energy is added to it. In addition, if energy is transferred out of a system to its surroundings, the system will cool and the pressure within it will decrease.

The First Law also forms the basis of the Zeroth Law of Thermodynamics, which states that two systems in thermal equilibrium with a third system, must be in thermal equilibrium with each other. This means that two bodies in contact will eventually reach the same temperature. This means that the thermal energy that exists between two systems can either be exchanged or released depending on whether it is higher or lower than the equilibrium temperature.

The importance of the First Law of Thermodynamics is in its ability to serve as a fundamental check for energy conservation in physical systems. It serves as a fundamental law to which all other laws of thermodynamics must agree with, and its statement is so simple that it is often used in introductory courses in thermodynamics. By understanding the First Law, scientists and engineers are able to develop systems and processes that are more efficient and use less energy in the long run.

The first law of thermodynamics is also important for analyzing energy transfer in the environment. Since energy can neither be created nor destroyed, altering the heat energy in one part of the environment will transfer to other parts, thus affecting the temperature, pressure, and density of the environment. This is key in current debates on climate change as it explains how carbon dioxide and other greenhouse gases in the atmosphere can trap heat and cause global warming.

The First Law of Thermodynamics is a cornerstone of understanding the transfer of energy in physical systems and plays a key role in many scientific studies. Its implications on energy conservation, the environment, and climate change are still expanding, making it an important part of research and an invaluable tool to help us gain a better understanding of the physical world around us.

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macroeconomic 748 2023-07-03 1035 CrystalineAura

The Pythagorean Theorem is one of the most well-known and widely-used mathematical theorems. It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In other word......

The Pythagorean Theorem is one of the most well-known and widely-used mathematical theorems. It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In other words, given a right triangle with sides of length a, b and c (from a short side to the hypotenuse), the Pythagorean Theorem says that

a2 + b2 = c2

This theorem is named after the Greek mathematician, Pythagoras, who is credited for discovering the theorem in the 6th century BC. Despite its ancient origins, the Pythagorean Theorem is still a widely used result, particularly in fields such as engineering, navigation, architecture and surveying.

The theorem can be used to calculate the lengths of sides in a right triangle. For example, if two sides in a triangle are known (say, 4 cm and 5 cm), the length of the third side can be calculated using the theorem: 42 + 52 = c2. Rearranging, c2 = 41, so c = √41 ≈ 6.4 cm.

The theorem can also be used to determine whether a given triangle is a right triangle. For example, if three sides lengths are given (say, 7 cm, 24 cm and 25 cm), the Pythagorean Theorem can be used to check if the triangle formed is right. Substituting the sides lengths into the theorem gives: 72 + 242 = 252. This equation is satisfied, so the triangle is a right triangle - the side lengths fulfil the theorem exactly.

The Pythagorean Theorem might be one of the oldest theorems still in use, but it is still incredibly useful and important to many applications.

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