Cecily Zamora
The first law of thermodynamics, also known as the Law of Conservation of Energy, states that energy cannot be created or destroyed. It can only be transferred or changed from one form to another. This law is fundamental to all scientific and engineering applications. The adiabatic form of the first law of thermodynamics refers to closed systems and asserts the existence of internal energy as a function of state defined in terms of adiabatic work. In an adiabatic process, no heat is exchanged with the surroundings, and the work done on the system depends on the end states only.
| Characteristics | Values |
|---|---|
| First Law of Thermodynamics | Energy cannot be created or destroyed in an isolated system |
| Energy can only be transferred or changed from one form to another | |
| Adiabatic Process | No heat transfer or work |
| Net internal energy change of the system is zero | |
| Work done by the system entirely depends on change in internal energy of the system | |
| Work done in an adiabatic process between two given end states depends on end states only | |
| Temperature changes can be quantified using the ideal gas law | |
| No truly adiabatic processes occur |
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What You'll Learn
Adiabatic free expansion of an ideal gas
Adiabatic processes are those in which there is no transfer of heat to or from a system, so that Q = 0. In the context of the first law of thermodynamics, this means that the quantity of energy added to a system as heat is zero.
An example of an adiabatic process is the free expansion of an ideal gas. This can be demonstrated by considering a rigid container that is thermally insulated and divided into two compartments separated by a valve. One compartment contains the gas under investigation, while the other compartment is empty. When the valve is opened, the gas is free to expand and fill the entire container.
During the free expansion of an ideal gas, the gas does work and its temperature drops. This is because the gas expands against a vacuum, resulting in zero external pressure. As a result, the work done by the system is zero, and because the vessel is thermally insulated, the expansion is adiabatic.
The first law of thermodynamics 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. In the case of adiabatic free expansion, since there is no heat added to the system and no work done by the system, the change in internal energy is zero. This implies that the internal energy of the gas remains constant during the expansion.
It is important to note that the free expansion of a gas is an irreversible process. This means that while the initial and final temperatures of the gas may be the same, the temperature remains undefined and variable throughout the process. Therefore, it is incorrect to assume that the free expansion of a gas is an isothermal process, as the temperature is not constant.
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Adiabatic curve
An adiabatic process is a type of thermodynamic process that occurs without the transfer of heat between the system and its environment. In other words, it is a process without heat transfer to or from a system, so that Q = 0, and such a system is said to be adiabatically isolated. The first law of thermodynamics, a restatement of the law of conservation of energy, is supported by the adiabatic process. This law states that energy cannot be created or destroyed in an isolated system, but it can be transferred or changed from one form to another.
An adiabatic curve, also known as a "curve of no transmission of heat", is a curve of constant entropy in a diagram. It was first described by Rankine in 1854, who used a quantity he called "the thermodynamic function", which later became known as entropy. Adiabatic curves have two isothermal limbs, and they are similar to isotherms, except that during an expansion, an adiabat loses more pressure than an isotherm, resulting in a steeper inclination.
Adiabatic processes can be observed in the compression of a gas within a cylinder of an engine, where the compression occurs so rapidly that there is no time for the gas to exchange heat with its surroundings. This is also seen in the free expansion of a gas, where the gas is contained in an insulated container and allowed to expand into a vacuum, with no external pressure to work against.
The mathematical equation for an ideal gas undergoing a reversible adiabatic process can be represented by the polytropic process equation, and the process is often illustrated on a P-V diagram, where it is differentiated from an isothermal process by its steeper slope.
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Adiabatic expansion and contraction
Adiabatic processes are a key concept in thermodynamics, and they support the theory behind the first law of thermodynamics. In an adiabatic process, there is no transfer of heat between the system and its environment. Instead, energy is transferred to the surroundings as work and/or mass flow.
Adiabatic expansion occurs when the pressure on an adiabatically isolated system is decreased, allowing it to expand in size and do work on its surroundings. This can be seen in the Earth's atmosphere with orographic lifting and lee waves, which can form pilei or lenticular clouds. Adiabatic expansion can be used to reach very low temperatures through adiabatic demagnetisation, where the change in magnetic field causes adiabatic expansion in a magnetic material.
Adiabatic expansion can also be observed in the free expansion of an ideal gas. When a gas is confined to one side of a thermally insulated container, it remains in place until the membrane is punctured, at which point the gas rushes into the empty side of the container, expanding freely. This process does no work because the gas expands against a vacuum, and it is adiabatic because the vessel is thermally insulated.
Adiabatic expansion can also be achieved through a quasi-static process. An insulated cylinder containing an ideal gas can be made to expand quasi-statically by removing one grain of sand at a time from the top of the piston. As the gas expands, its temperature decreases, and work is done by the gas in the expansion.
Adiabatic compression, the opposite of adiabatic expansion, occurs when the pressure of a gas is increased, causing a decrease in volume and an increase in temperature. This can be seen in the cylinders of a car, where the compression of the gas-air mixture occurs so quickly that there is no time for heat exchange with the environment. However, because work is done on the mixture during compression, its temperature rises significantly, and the mixture may even explode without a spark, causing the car to run poorly.
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Adiabatic compressions in car cylinders
The first law of thermodynamics is a restatement of the law of conservation of energy. It states that energy cannot be created or destroyed in an isolated system, but it can be transferred or changed from one form to another. An adiabatic process is one in which there is no transfer of heat to or from the system (Q = 0).
Adiabatic compression occurs when the pressure of a gas is increased by the work done on it by its surroundings, for example, a piston compressing a gas contained within a cylinder. This is relevant to car cylinders because adiabatic compressions occur in the cylinders of a car engine. The compression of the gas-air mixture takes place very quickly, leaving no time for the mixture to exchange heat with its environment. However, work is done on the mixture during the compression, so its temperature rises significantly. This temperature increase can cause the mixture to explode without a spark, which can make a car run poorly. This is known as "knocking". One way to overcome this problem is to use higher-octane gasoline, as the ignition temperature rises with the octane level of gasoline.
In a diesel engine, the fuel is ignited without a spark plug. Instead, air in a cylinder is compressed adiabatically to a temperature above the ignition temperature of the fuel. At the point of maximum compression, the fuel is injected into the cylinder. Diesel engines operate under extreme conditions, with compression ratios of 16:1 or higher, to provide a very high gas pressure that ensures immediate ignition of the injected fuel.
In practice, no process is truly adiabatic as there is always some heat loss due to the absence of perfect insulators. However, the assumption of adiabatic isolation is useful for calculating a good first approximation of a system's behaviour. For example, the compression of a gas within a cylinder is often assumed to be adiabatic, even though the cylinders are not insulated and are quite conductive.
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Adiabatic assumption
The adiabatic assumption is a key concept in thermodynamics, supporting the theory that explains the first law of thermodynamics. The first law of thermodynamics is a restatement of the law of conservation of energy. It states that energy cannot be created or destroyed in an isolated system; energy can only be transferred or changed from one form to another.
An adiabatic process is a type of thermodynamic process that occurs without transferring heat between the system and its environment. The term adiabatic is derived from the Ancient Greek word "adiábatos," meaning impassable. This is distinct from an isothermal process, which allows for the transfer of heat.
In an adiabatic process, energy is transferred only as work and/or mass flow. A process without the transfer of heat to or from a system, where Q (the quantity of energy added as heat) is equal to zero, is called adiabatic. Such a system is said to be adiabatically isolated.
While no process is truly adiabatic, many processes rely on a large difference in time scales between the process of interest and the rate of heat dissipation across a system boundary. This allows for the use of an adiabatic assumption, which is a useful simplification. For example, the compression of a gas within a cylinder of an engine is assumed to occur so rapidly that, on the timescale of the compression process, little energy can be transferred out as heat to the surroundings. This assumption of adiabatic isolation is often combined with other idealizations to calculate a good first approximation of a system's behaviour.
Adiabatic processes have practical applications, such as in the compression stroke of a gasoline engine and the free expansion of a gas.
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Frequently asked questions
The adiabatic form of the first law of thermodynamics states that for an isolated system, energy cannot be created or destroyed, only transferred or changed from one form to another. In other words, the law of conservation of energy.
An example of an adiabatic process is the free expansion of a gas. When a gas is confined to one side of a two-compartment, thermally insulated container, and the membrane is punctured, the gas rushes into the empty side, expanding freely. This is also known as a Joule expansion.
The first law of thermodynamics can be written as ΔU = Q − W, where ΔU is the change in internal energy, Q is the quantity of heat added, and W is the work done by the system. In an adiabatic process, Q = 0, so the first law becomes ΔU = 0 + W. This means that the net internal energy change of the system is zero.
