
The first law of thermodynamics is a version of the law of conservation of energy, which states that energy can be transformed from one form to another but cannot be created or destroyed. The first law of thermodynamics applies this principle to thermodynamic processes, stating that when energy passes into or out of a system as work, heat, or matter, the system's internal energy changes in accordance with the law of conservation of energy. This law also states that in an externally isolated system, the sum of all forms of energy must remain constant. However, the first law of thermodynamics does not account for certain factors, and there are aspects that are not part of this law.
| Characteristics | Values |
|---|---|
| Scope | The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes. |
| Definition | When energy passes into or out of a system (as work, heat, or matter), the system's internal energy changes in accordance with the law of conservation of energy. |
| Formula | ΔU = Q - W, where ΔU is the change in internal energy of the system, Q is the heat supplied to the system, and W is the work done by the system on its surroundings. |
| Closed System | In a closed system, there is no transfer of matter into or out of the system, only changes in internal energy. |
| Open System | In an open system, there can be transfers of particles and energy into or out of the system during a process. |
| Perpetual Motion | It is not possible to construct a perpetual motion machine of the first kind, i.e., a machine that outputs work without an equal amount of energy input. |
| Heat and Work | Heat and work are forms of energy in transition and do not describe the state of a system; they are path functions, not state functions. |
| Energy Conservation | The total energy of an isolated system remains constant; energy can be transformed but not created or destroyed. |
| Historical Notes | The first law was formulated by scientists such as Rudolf Clausius and William Thomson by 1860. |
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What You'll Learn

Energy conservation
The first law of thermodynamics, also known as the law of energy conservation, states that the total energy of an isolated system remains constant. When energy enters or leaves a system in the form of work, heat, or matter, the system's internal energy changes accordingly. This law was formulated by scientists such as Rudolf Clausius and William Thomson in the 19th century and is expressed in two ways for closed systems. One approach considers cyclic processes and the inputs and outputs without addressing changes in the system's internal state.
The other expression of the law for closed systems involves the concept of internal energy (ΔU). In this case, the change in internal energy of the system (ΔUsystem) equals the heat supplied (Q) minus the work done by the system (W). It is important to distinguish between heat and internal energy, as the former represents energy in transition at the system's boundary, while the latter is the energy associated with the random molecular motion of the system's constituents.
For open systems, where matter and energy can enter or exit, the first law still applies, but additional considerations come into play. The transfer of matter between two systems is accompanied by a transfer of internal energy that cannot be solely attributed to heat and work. This law also accounts for pathways that allow heat and work transfer independent of matter transfer.
The first law of thermodynamics has important implications, such as precluding the possibility of perpetual motion machines. It also provides a foundation for understanding and optimizing energy utilization in various processes, allowing for comparisons between different systems and guiding improvements.
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Heat and work
Heat is the transfer of thermal energy between two bodies at different temperatures. It is produced by friction and percussion, which are forms of dissipation of "motive power". Work, on the other hand, is the force used to transfer energy between a system and its surroundings, and it is required to generate heat and transfer thermal energy. Work is the motion against an opposing force, and its magnitude depends on the mass of the object, the strength of the opposing force, and the distance through which the force acts. For example, lifting a weight against the force of gravity requires work.
In a closed system, the first law of thermodynamics states that the change in internal energy of the system (ΔU) is equal to the difference between the heat supplied to the system (Q) and the work (W) done by the system on its surroundings. This can be expressed mathematically as δQ + δW = ΔE, where δ denotes infinitesimal changes. In a reversible process, such as the expansion or contraction of fluid boundaries, the work done per unit mass can be calculated as -pdυ, where p is pressure, υ is specific volume, and dυ is the change in specific volume.
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Open and closed systems
The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes. This law states that when energy passes into or out of a system (as work, heat, or matter), the system's internal energy changes in accordance with the law of conservation of energy.
Now, a thermodynamic system can be an open system or a closed system. The first law of thermodynamics for closed systems involves the distinction between transfers of energy as work and as heat. For closed systems, the concepts of an adiabatic enclosure and an adiabatic wall are fundamental. Matter and internal energy cannot permeate or penetrate such a wall.
The first law of thermodynamics for a closed system was expressed in two ways by Clausius. One way referred to cyclic processes and the inputs and outputs of the system, but did not refer to increments in the internal state of the system. In the case of a closed system, the particles of the system are of different types, and their respective numbers are not necessarily constant due to chemical reactions. The fundamental thermodynamic relation for dU is influenced by the increase in the number of type-i particles in the reaction and the chemical potential of these particles.
For an open system, there can be transfers of particles as well as energy into or out of the system during a process. An open system is not adiabatically enclosed, and matter can pass between the system and its surroundings. There are cases where a process for an open system can be considered a closed system, such as when there is no actual passage of matter.
The first law of thermodynamics for open systems involves transfers between two otherwise isolated open systems. When two systems with internal energies U1 and U2 are combined to produce a new system with internal energy U, the reference states for U, U1, and U2 should be specified, maintaining that the internal energy of a system is proportional to its mass.
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Perpetual motion
The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes. In general, the conservation law states that the total energy of an isolated system remains constant; energy can be transformed from one form to another but can be neither created nor destroyed. The first law of thermodynamics states that when energy passes into or out of a system (as work, heat, or matter), the system's internal energy changes in accordance with the law of conservation of energy. This results in the observation that, in an externally isolated system, even with internal changes, the sum of all forms of energy must remain constant as energy cannot be created or destroyed.
The first law of thermodynamics also states that it is not possible to construct a machine that will perpetually output work without an equal amount of energy input into that machine. This is also known as a perpetual motion machine of the first kind.
Despite the scientific consensus, many have attempted to create perpetual motion machines. In the mid-19th century, Henry Dircks investigated the history of perpetual motion experiments, writing a scathing attack on those who continued to attempt what he believed to be impossible. Modern designers and proponents often use other terms, such as "over unity", to describe their inventions.
There are three kinds of perpetual motion devices. The first kind includes devices that purport to deliver more energy from a falling or turning body than is required to restore those devices to their original state. The second kind attempts to violate the second law of thermodynamics—namely, that some energy is always lost in converting heat into work. The third kind is defined as one that completely eliminates friction and other dissipative forces, to maintain motion forever due to its mass inertia.
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Internal energy
The first law of thermodynamics states that the total energy of an isolated system remains constant. In other words, energy cannot be created or destroyed, only transformed from one form to another. This is also known as the law of conservation of energy.
The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system and the work done on the system. Mathematically, this can be expressed as:
\[ \Delta U = Q + W \]
Where:
- \(\Delta U\) is the change in internal energy of the system
- \(Q\) is the heat added to the system
- \(W\) is the work done on the system
It's important to distinguish between internal energy and heat. Heat is a form of energy in transition, appearing at the boundary of the system, while internal energy is a function of state, depending on factors such as pressure, volume, and temperature. For example, in the case of a gas, its internal energy is uniquely determined by its pressure, volume, and temperature.
In summary, the first law of thermodynamics relates to the conservation of energy, and internal energy is a critical aspect of this law, representing the total energy within a system. Understanding the interplay between internal energy, heat, and work allows for the analysis and prediction of energy transfers and changes within thermodynamic systems.
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