# First Law of Thermodynamics

The First Law of Thermodynamics is a crucial concept in thermodynamics. It's one of the three fundamental laws that govern energy. The law is based on the idea that energy cannot be created or destroyed, only transferred or transformed. This is especially important when considering systems that transfer energy through heat and work. Understanding the First Law of Thermodynamics is essential for anyone interested in the science of energy.

## The first law of thermodynamics: Equation

The First Lawodynamics was first in the 19th century by Rudolf Clausius and William Thomson. The law states that in a closed system, the total change in internal energy (ΔU) is equal to the amount of heat transferred into the system (Q) minus the total work done by the system (W). This means that the energy of a system is always conserved, and that any changes in the system's energy can be accounted for by the transfer of heat or the performance of work. Understanding this fundamental law is essential for anyone interested in the science of thermodynamics.

### First law of thermodynamics: Internal energy (U)

To understand the internal energy of a system, it's important to consider the kinetic and potential energy of the atoms and molecules that make up the system. However, it's often more useful to define the internal energy on a larger scale, using macroscopic quantities such as pressure, temperature, and volume. By studying these properties, we can gain a better understanding of the behavior of the system as a whole.

When heat is added to a system or work is done on the system, the internal energy can become positive. On the other hand, when heat is removed from the system or work is done by the system on its surroundings, the internal energy can become negative. Understanding these changes in internal energy is important in a variety of scientific fields, from thermodynamics to materials science.

### First law of thermodynamics: Heat (Q)

Heat (Q) is a form of energy that is transferred between two objects or systems due to a difference in temperature. This transfer occurs through molecular motion and collisions, and it is measured in joules.

When the system is taken as the reference, the heat that enters a system can be considered to be positive because it increases the internal energy of the system. On the other hand, the heat that exits a system is considered to be negative because it decreases the internal energy of the system.

Understanding the transfer of heat is important in a variety of fields, from engineering to physics to biology. In many cases, it is necessary to control the flow of heat in order to optimize the performance of a system or to prevent damage to materials or organisms.

### First law of thermodynamics: Work (W)

The work (W) of a system is a measure of the energy that is transferred between the system and its surroundings. This transfer can occur in a variety of ways, including through mechanical processes such as pushing or pulling. Work is measured in joules and is a general form of mechanical energy.

When the system of reference does work on an external system, the work is considered positive because energy is added to the system of reference. Conversely, when the system of reference loses energy to an external system, the work is considered negative.

Some examples of positive and negative work depending on the chosen system of reference are as follows:

• Positive work: A person lifts a box off the ground, increasing its potential energy. The system of reference is the person doing the lifting, and work is done on the box.
• Negative work: A ball rolls down a hill, losing potential energy as it gains kinetic energy. The system of reference is the ball, and work is done by the ball on the surroundings as it rolls down the hill.

Understanding the work done by a system is crucial in many fields, including physics, engineering, and chemistry, as it can help us to understand the transfer of energy between different systems.

### First law of thermodynamics in differential form

The differential form of the first law of thermodynamics is an important equation used to describe the rate of change of a system's internal energy. The equation can be expressed as:

∂ U = ∂ Q - ∂ W

where ∂U is the change in internal energy of the system, ∂Q is the heat added to the system, and ∂W is the work done by the system.

In the case of a hydrostatic system containing fluids, the equation can be simplified to:

dU = dQ - pdV

where dU is the change in internal energy, dQ is the heat added to the system, p is the pressure, and dV is the change in volume of the system.

The negative sign in the equation indicates that the changes in volume are always opposite in sign to the changes in work. For example, if work is positive, meaning energy is added to the system, then dV would be negative, indicating a decrease in volume. Conversely, if work is negative, meaning energy is lost from the system, then dV would be positive, indicating an increase in volume.

Understanding the first law of thermodynamics and its differential form is crucial in fields such as engineering and physics, as it provides a framework for analyzing energy transfer and conversion in a wide range of systems.

### First law of thermodynamics examples

The most common application of the first law of thermodynamics is the heat engine, which is used in trains, vehicles, etc. Other applications include aeroplane engines, refrigerators systems, and heat pumps. How much work is done by a gas that is compressed from 35L to 15L under a constant external pressure of 3 atm? Solution: ∂ W = - p ∂ V = - p · (  V f  - V    i  ) As the gas is compressed, the work is positive, and dV is negative: ∂ W   =   - 3 a t m ·   ( 15 L - 35 L )   =   60 L a t m As we need to convert this to Joules, we multiply by the gas constant J/mol K and divide by the gas constant 0.08206 L atm/mol K.   L a t m ·   J  m o l · K    L a t m   m o l · K  ∂ W =   60   a t m · 8 . 31447   J / m o l · K   0 . 08206   L · a t m / m o l · K   = 6079   J

### First law of thermodynamics: Thermodynamic systems

Thermodynamics is concerned with the study of energy transfer and conversion in different systems. In this field, there are three types of systems that can be observed:

1. Open systems: These are systems that exchange both energy and matter with their surroundings. In other words, they can take in or give out both energy and matter. An example of an open system is boiling water in a pan. As the water boils and turns into steam, energy and matter are transferred from the pan to the surrounding atmosphere as steam.
2. Closed systems: These are systems that exchange only energy with their surroundings. In other words, they can take in or give out energy, but not matter. A common example of a closed system is a hot cup of coffee with a lid on. As the coffee cools down, energy is transferred from the coffee to the surrounding atmosphere in the form of steam.
3. Isolated systems: These are a special case of closed systems that transfer neither energy nor matter to other systems or their surroundings. In other words, they do not interact in any way with their surroundings. An example of an isolated system is a perfectly insulated and closed nitrogen tank. Such a tank is designed to transfer neither energy nor matter to its surroundings.

Understanding the different types of systems in thermodynamics is important in the study of energy transfer and conversion. It helps to determine the direction and magnitude of heat and work that can be exchanged between the system and its surroundings.

## How does the first law of thermodynamics apply to gases?

Gases are highly sensitive to changes in macroscopic quantities such as volume, temperature, and density. When the temperature of a gas increases, it tends to expand due to the increased kinetic energy of the gas molecules. Conversely, when the temperature decreases, gases tend to compress.

For constant pressure, the formula W = -p·ΔV be used to calculate the work done by or on a gas. Here, W represents work, p represents pressure, and ΔV represents the change in volume. The minus sign indicates that the work is done with respect to the system.

When a gas expands, energy is transferred to the system's surroundings, and work is done by the gas on the surroundings. In this case, the work is negative (-W) with respect to the system (gas) since energy is released from the system.

When a gas is compressed, energy is transferred from the surroundings to the gas, and work is done on the gas by the surroundings. Hence, the work is positive (+W) with respect to the system (gas). If the work done is being considered with respect to the surroundings, then the sign in the equation becomes positive. Work done becomes positive when the gas is expanded, while the work done is negative when the gas is compressed.

In summary, thermodynamics is concerned with the study of energy, heat, and temperature of matter. The first law of thermodynamics was derived from the conservation of energy theorem and states that changes in internal energy are equal to the work done subtracted by heat addition. The most common application of the first law of thermodynamics is the heat engine. Understanding these concepts is important in various fields, such as engineering and physics, where energy transfer and conversion play a crucial role.

## First Law of Thermodynamics

What is the first law of thermodynamics?

The first law of thermodynamics states the relationship between the change in total internal energy of a system, the heat addition, and the work done. This can be mathematically expressed as ΔU = Q - W. Here, ΔU is the change in internal energy, Q is the heat added to the system, and W is work done by the system.

What quantities appear in the first law of thermodynamics?

Heat (Q), work (W), and the change in total energy (ΔU).

Which physical law underlies the first law of thermodynamics?

The law of the conservation of energy.

Who discovered the first law of thermodynamics?

Rudolf Clausius and William Thomson stated the first law of thermodynamics in 1865.

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