Isothermal process

# Isothermal process

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An isothermal process is a change of a system, in which the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

exchange. In contrast, an adiabatic process
In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...

is where a system exchanges no heat with its surroundings
Surroundings
Surroundings are the area around a given physical or geographical point or place. The exact definition depends on the field. Surroundings can also be used in geography and mathematics, as well as philosophy, with the literal or metaphorically extended definition.In thermodynamics, the term is used...

(Q = 0). In other words, in an isothermal process, the value ΔT = 0 but Q ≠ 0, while in an adiabatic process, ΔT ≠ 0 but Q = 0.

## Details for an ideal gas

For the special case of a gas to which Boyle's law
Boyle's law
Boyle's law is one of many gas laws and a special case of the ideal gas law. Boyle's law describes the inversely proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system...

applies, the product pV is a constant if the gas is kept at isothermal conditions. The value of the constant is nRT, where n is the number of moles of gas present and R is the ideal gas constant. In other words, the ideal gas law
Ideal gas law
The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...

pV = nRT applies. This means that

holds. The family of curves generated by this equation is shown in the graph presented at the bottom right-hand of the page. Each curve is called an isotherm. Such graphs are termed indicator diagrams and were first used by James Watt and others
James Watt
James Watt, FRS, FRSE was a Scottish inventor and mechanical engineer whose improvements to the Newcomen steam engine were fundamental to the changes brought by the Industrial Revolution in both his native Great Britain and the rest of the world.While working as an instrument maker at the...

to monitor the efficiency of engines. The temperature corresponding to each curve in the figure increases from the lower left to the upper right.

## Calculation of work

In thermodynamics, the work involved when a gas changes from state A to state B is simply

For an isothermal, reversible
Reversible process (thermodynamics)
In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy. Due to these infinitesimal changes, the system is in thermodynamic...

process, this integral equals the area under the relevant pressure-volume isotherm, and is indicated in blue in the figure (at the bottom right-hand of the page) for an ideal gas. Again, p = nRT / V applies and with T being constant (as this is an isothermal process), we have:

By convention, work is defined as the work the system does on its environment. If, for example, the system expands by a piston moving in the direction of force applied by the internal pressure of a gas, then the work is counted as positive, and as this work is done by using internal energy of the system, the result is that the internal energy decreases. Conversely, if the environment does work on the system so that its internal energy increases, the work is counted as negative.

It is also worth noting that, for many systems, if the temperature is held constant, the internal energy of the system also is constant, and so . From First Law of Thermodynamics
First law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...

, , so it follows that for this same isothermal process.

## Applications

Isothermal processes can occur in any kind of system, including highly-structured machines, and even living
Life
Life is a characteristic that distinguishes objects that have signaling and self-sustaining processes from those that do not, either because such functions have ceased , or else because they lack such functions and are classified as inanimate...

cells. Various parts of the cycles of some heat engine
Heat engine
In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance...

s are carried out isothermally and may be approximated by a Carnot cycle
Carnot cycle
The Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded by Benoit Paul Émile Clapeyron in the 1830s and 40s. It can be shown that it is the most efficient cycle for converting a given amount of thermal energy into work, or conversely,...

. Phase changes, such as melting
Melting
Melting, or fusion, is a physical process that results in the phase change of a substance from a solid to a liquid. The internal energy of a substance is increased, typically by the application of heat or pressure, resulting in a rise of its temperature to the melting point, at which the rigid...

or evaporation
Evaporation
Evaporation is a type of vaporization of a liquid that occurs only on the surface of a liquid. The other type of vaporization is boiling, which, instead, occurs on the entire mass of the liquid....

, are also isothermal processes.

In Isothermal non flow Process, the work done by compressing the perfect gas (Pure Substance) is a negative work, as work is done on the system, as result of compression, the volume will decrease, and temperature will try to increase. To maintain the temperature at constant value (as the process is isothermal) heat energy has to leave the system and enter the environment. The amount of energy entering the environment is equal to the work done (by compressing the perfect gas) because internal energy does not change. The thermodynamic sign convention is that heat entering the environment is also negative. Thence Q = W.

In equation of work, the term nRT can be replaced by PV of any state. The product of pressure and volume is in fact, 'Moving Boundary Work'; the systems boundaries are compressed. For Expansion the same theory is applied.

As per Joule's Law, Internal energy is the function of absolute temperature. In isothermal process the temperature is constant. Hence, the internal energy is constant. And net change in internal energy is ZERO.