First Law of Thermodynamics: Derivation, Applications and Limitations

State First Law of Thermodynamics

Energy cannot be generated or destroyed; rather, it can only be changed from one form to another, according to the first law of thermodynamics. It is often expressed in the form of a mathematical equation and has a vast use in the GATE exam, which states that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings. This equation can be written as:

ΔU = Q – W

where

• ΔU is the change in the system’s internal energy,
• Q is the heat added to the system, and
• W is the work the system does on its surroundings.

The first law of thermodynamics is a fundamental law of physics similar to the zeroth law of thermodynamics. This law applies to all physical systems, including thermodynamic systems. It is an important law used to understand systems’ behaviour and design new energy technologies and devices. It is also known as the law of energy conservation or the principle of energy conservation.

Derivation of the First Law of Thermodynamics

The first law of thermodynamics can be derived from energy conservation, which states that energy cannot be created or destroyed, only converted from one form to another. The first law of thermodynamics is often expressed in terms of the change in the internal energy of a system, which is the sum of the kinetic and potential energies of the particles within the system.

The change in the internal energy of a system can be expressed as the difference between the system’s initial and final internal energies. If U_i denotes the initial internal energy of the system and U_f denotes the final internal energy of the system, then the change in the internal energy of the system is given by:

ΔU = U_f – U_i

The change in the internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings. If the heat added to the system is denoted by Q and the work done by the system on its surroundings is denoted by W, then the change in the internal energy of the system is given by:

ΔU = Q – W

This relationship can be written as a mathematical equation known as the first law of thermodynamics, which states that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings. This equation allows us to understand a thermodynamic system’s behavior and predict the changes in energy that will occur during various processes. Overall, the first law of thermodynamics can be derived from the law of energy conservation and is a statement of the relationships between heat, work, and internal energy in a thermodynamic system. It is a fundamental law of physics used to understand the behavior of thermodynamic systems and to design new technologies and devices that use energy.

First Law for a Closed System Undergoing a Cycle

In a closed system undergoing a cycle, the first law of thermodynamics states that the heat added to the system, Q, is equal to the work done by the system on its surroundings, W, plus the change in the internal energy of the system, ΔU. This relationship can be written as:

Q = W + ΔU

A cycle is a process that returns a system to its initial state after it has undergone a series of changes. In a closed system undergoing a cycle, the internal energy of the system changes due to the addition or removal of heat and the work done by the system on its surroundings. The first law of thermodynamics can be used to predict the changes in internal energy and the heat added or removed from the system during a cycle.

For example, in a closed system undergoing a cycle, the first law of thermodynamics can be used to predict the efficiency of a heat engine, such as an internal combustion engine or a steam turbine. The efficiency of a heat engine is defined as the ratio of the work done by the engine to the heat added to the system. The first law of thermodynamics can be used to calculate the efficiency of a heat engine by determining the heat added to the system and the work done by the system on its surroundings during a cycle.

(ΣW)_cycle = J(Q)_cycle

where J is Joule’s equivalent. This is also expressed in the form

∮dW = ∮dQ

Fig.1: Closed System Undergoing A Cycle

First Law for a Closed System Undergoing a Change of State(for a process):

A change of state refers to a process in which a substance changes from one state of matter (such as solid, liquid, or gas) to another. In a closed system undergoing a change of state, the system’s internal energy changes due to the addition or removal of heat and the work done by the system on its surroundings. The first law of thermodynamics can be used to predict the changes in internal energy and the heat added or removed from the system during a change of state.

The expression:

(ΣW)_cycle = J(Q)_cycle

The above equation applies only to systems undergoing cycles, with zero algebraic sum of all energy interaction across system boundaries.

If both heat transfer and work transfer are involved in a change of state of the system, then the net energy transfer will be stored or accumulated within the system.
If heat transferred to the system is Q and work transferred from the system is W, during the process

Then, net energy transfer (Q – W) will be stored in the system.

Energy in storage is not in the form of heat and work it is simply the energy of the system, thus referred to as the internal energy of the system.

Therefore: Q – W – ΔE

where ΔE: Increase in the system’s energy.

Q = ΔE + W

Significance of the First Law of Thermodynamics

The first law of thermodynamics is a fundamental law of physics that has significant implications for various fields and applications. It is a key law used to understand the behaviour of thermodynamic systems and to design new technologies and devices that use energy. One of the most important applications of the first thermodynamics law is energy production and utilization. The first law of thermodynamics is used to predict the efficiency of energy conversion processes, such as converting heat to mechanical work in a steam turbine or converting chemical energy to electrical energy in a battery. This law is also used to understand the performance of engines and to design more efficient and effective energy-producing technologies.

In addition to its applications in energy production, the first law of thermodynamics is also important in understanding the behavior of physical systems in general. It is used to predict the changes in energy that will occur during various processes and to understand the relationships between energy, work, and heat. The first law of thermodynamics is also used to understand the behaviour of gases and other substances under different conditions, such as temperature and pressure. Overall, the first law of thermodynamics is a fundamental law of physics that has significant implications for many fields and applications. It is an important law; MSQ-based questions are seen in the GATE ME question papers and used to understand the behaviour of physical systems and to design new technologies and devices that use energy.

Applications of the First Law of Thermodynamics

The first law of thermodynamics has a wide range of applications in various fields and industries. Some examples of the applications of the first law of thermodynamics include:

1. Energy production and utilization: The first law of thermodynamics is used to predict the efficiency of energy conversion processes, such as converting heat to mechanical work in a steam turbine or converting chemical energy to electrical energy in a battery. It is also used to understand the performance of engines and to design more efficient and effective energy-producing technologies.
2. Refrigeration and air conditioning: The first law of thermodynamics is used to understand the behavior of refrigerants and to design refrigeration and air conditioning systems that are efficient and effective at cooling.
3. Heat transfer: The first law of thermodynamics is used to understand the behavior of heat transfer processes, such as conduction heat transfer, convection heat transfer, and radiation heat transfer. It is used to design heat exchangers and other devices that transfer heat from one location to another.
4. Chemical reactions: The first law of thermodynamics is used to understand the behavior of chemical reactions and predict the energy changes that will occur during a chemical reaction.
5. Thermodynamics of gases: The first law of thermodynamics is used to understand the behavior of gases and to predict the changes in temperature, pressure, and volume that will occur during different processes.
6. Biological systems: The first law of thermodynamics is used to understand the behavior of biological systems, such as the metabolism of living organisms. It is also used to design devices and technologies used in medicine, such as pacemakers and artificial organs.

Overall, the first law of thermodynamics has a wide range of applications in various fields and industries. It is an important law used to understand the behavior of physical systems and to design new technologies and devices that use energy.

Limitations of the First Law of Thermodynamics

While the first law of thermodynamics is a fundamental law of physics that is widely accepted and has many important applications, it does have some limitations. Some of the limitations of the first law of thermodynamics include the following:

1. It does not provide information about the direction of energy flow: The first law of thermodynamics only describes the conservation of energy and the relationships between heat, work, and internal energy. It does not provide information about the direction in which energy will flow or the rate at which energy will be transferred.
2. It does not take into account changes in entropy: The first law of thermodynamics does not take into account changes in entropy, which is a measure of the disorder or randomness of a system. The second law of thermodynamics, which is a separate law, deals with changes in entropy and the direction of energy flow.
3. It does not provide a complete description of the behaviour of physical systems: The first law of thermodynamics only describes the conservation of energy and the relationships between heat, work, and internal energy. It does not provide a complete description of the behaviour of physical systems and does not consider other factors, such as the motion and interactions of particles.
4. It does not provide information about the ultimate fate of energy: The first law of thermodynamics only describes the conservation of energy and the relationships between heat, work, and internal energy. It does not provide information about the ultimate fate of energy or the ultimate destiny of the universe.

Overall, while the first law of thermodynamics is a fundamental law of physics with many important applications, it does have some limitations and does not provide a complete description of the behaviour of physical systems.

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