Isothermal Lines

The “isothermal process”, which is thermodynamic process in which the temperature of a system remains constant. The transfer of heat into or out of the system happens so slowly that thermal equilibrium is maintained. “Thermal” is a term that describes the heat of a system. “Iso” means “equal”, so “isothermal” means “equal heat”, which is what defines thermal equilibrium.

In general, during an isothermal process there is a change in internal energy, heat energy, and work, even though the temperature remains the same. Something in the system works to maintain that equal temperature. One simple ideal example is the Carnot Cycle, which basically describes how a heat engine works by supplying heat to a gas. As a result, the gas expands in a cylinder, and that pushes a piston to do some work. The heat or gas has to then be pushed out of the cylinder (or dumped) so that the next heat/expansion cycle can take place. This is what happens inside a car engine, for example. If this cycle is completely efficient, the process is isothermal because the temperature is kept constant while pressure changes.

To understand the basics of the isothermal process, consider the action of gases in a system. The internal energy of an ideal gas depends solely on the temperature, so the change in internal energy during an isothermal process for an ideal gas is also 0. In such a system, all heat added to a system (of gas) performs work to maintain the isothermal process, as long as the pressure remains constant. Essentially, when considering an ideal gas, work done on the system to maintain the temperature means that the volume of the gas must decrease as the pressure on the system increases.

Isothermal Processes and States of Matter

Isothermal processes are many and varied. Evaporation of water into the air is one, as is the boiling of water at a specific boiling point. There are also many chemical reactions that maintain thermal equilibrium, and in biology, the interactions of a cell with its surrounding cells (or other matter) are said to be an isothermal process.

Evaporation, melting, and boiling, are also “phase changes”. That is, they are changes to water (or other fluids or gases) that take place at constant temperature and pressure.

When scientists study isothermal processes in systems, they are really examining heat and energy and the connection between them and the mechanical energy it takes to change or maintain the temperature of a system. Such understanding helps biologists study how living beings regulate their temperatures. It also comes into play in engineering, space science, planetary science, geology, and many other branches of science. Thermodynamic power cycles (and thus isothermal processes) are the basic idea behind heat engines. Humans use these devices to power electrical generating Plants and, as mentioned above, cars, trucks, planes, and other vehicles. In addition, such systems exist on rockets and spacecraft. Engineers apply principles of thermal management (in other words, temperature management) to increase the efficiency of these systems and processes.

Example of isothermal process

Assume an isothermal expansion of helium (i → f) in a frictionless piston (closed system). The gas expansion is propelled by absorption of heat energy Qadd. The gas expands from initial volume of 0.001 m3 and simultaneously the external load of the piston slowly and continuously decreases from 1 MPa to 0.5 MPa. Since helium behaves almost as an ideal gas, use the ideal gas law to calculate final volume of the chamber and then calculate the work done by the system, when the temperature of the gas is equal to 400 K.

The final volume of the gas, Vf, can be calculated using p, V, T Relation for isothermal process:

piVi = pfVf ⇒ Vf = piVi / pf = 2 x 0.001 m3 = 0.002 m3

An isothermal process is a thermodynamic process in which the temperature of the system remains constant. This means that there is no heat transfer into or out of the system during the process. Isothermal processes are often used in engineering applications, such as in the design of refrigerators and air conditioners.

Isothermal lines are lines on a thermodynamic diagram that represent isothermal processes. They are horizontal lines on a pressure-volume diagram and vertical lines on a temperature-entropy diagram.

Isothermal expansion is a type of isothermal process in which the volume of the system increases. This can be done by adding heat to the system or by reducing the pressure on the system.

Isothermal compression is a type of isothermal process in which the volume of the system decreases. This can be done by removing heat from the system or by increasing the pressure on the system.

Isothermal work is the work done by a system during an isothermal process. It is equal to the product of the pressure and the change in volume.

Isothermal efficiency is the efficiency of a heat engine that operates in an isothermal cycle. It is equal to the work done by the engine divided by the heat input to the engine.

Isothermal heat transfer is the heat transfer that occurs between a system and its surroundings during an isothermal process. It is equal to the product of the specific heat capacity of the system and the change in temperature.

Isothermal reversible process is a type of isothermal process that is also reversible. This means that the process can be reversed by an infinitesimal change in the external conditions.

Isothermal irreversible process is a type of isothermal process that is not reversible. This means that the process cannot be reversed by an infinitesimal change in the external conditions.

Isothermal Carnot cycle is a theoretical thermodynamic cycle that is the most efficient heat engine cycle that can be operated between two given temperatures. It is a reversible cycle, which means that it can be reversed by an infinitesimal change in the external conditions.

Isothermal Otto cycle is a four-stroke internal combustion engine cycle that is used in gasoline engines. It is a modified version of the Carnot cycle that takes into account the compression and expansion of the air-fuel mixture in the cylinder.

Isothermal Diesel cycle is a four-stroke internal combustion engine cycle that is used in diesel engines. It is a modified version of the Otto cycle that takes into account the compression and expansion of the air in the cylinder.

Isothermal Brayton cycle is a thermodynamic cycle that is used in gas turbines. It is a modified version of the Carnot cycle that takes into account the compression and expansion of the air in the turbine.

Isothermal Rankine cycle is a thermodynamic cycle that is used in steam turbines. It is a modified version of the Carnot cycle that takes into account the compression and expansion of the steam in the turbine.

Isothermal Stirling cycle is a thermodynamic cycle that is used in Stirling engines. It is a modified version of the Carnot cycle that takes into account the compression and expansion of the working fluid in the engine.

What is a function?

A function is a mathematical relationship between two variables, such that each value of one variable determines a unique value of the other variable.

What is a graph?

A graph is a visual representation of a mathematical relationship between two variables. It is made up of points, which represent the values of the two variables, and lines, which connect the points.

What is a line?

A line is a one-dimensional figure that extends infinitely in both directions. It is the simplest type of curve.

What is a curve?

A curve is a one-dimensional figure that does not extend infinitely in both directions. It is a more complex type of figure than a line.

What is a surface?

A surface is a two-dimensional figure that extends infinitely in all directions. It is the simplest type of three-dimensional figure.

What is a volume?

A volume is a three-dimensional figure that extends infinitely in all directions. It is the simplest type of four-dimensional figure.

What is a derivative?

The derivative of a function is a measure of how much the function changes as its input changes. It is calculated using the limit definition of the derivative.

What is an integral?

The integral of a function is a measure of the area under the curve of the function. It is calculated using the fundamental theorem of calculus.

What is a limit?

A limit is a way of describing what happens to a function as its input approaches a certain value. It is calculated using the epsilon-delta definition of the limit.

What is a series?

A series is a sum of the terms of a sequence. It can be finite or infinite.

What is a sequence?

A sequence is a list of numbers that are ordered by their position in the list.

What is a Probability?

A probability is a measure of the likelihood of an event occurring. It is calculated using the formula $P(E) = \frac{n(E)}{n(S)}$, where $n(E)$ is the number of outcomes in the event and $n(S)$ is the total number of possible outcomes.

What is a statistics?

Statistics is the study of the collection, organization, analysis, interpretation, presentation, and Communication of data.

What is a linear equation?

A linear equation is an equation of the form $ax + by = c$, where $a$, $b$, and $c$ are real numbers and $a \neq 0$.

What is a quadratic equation?

A quadratic equation is an equation of the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are real numbers and $a \neq 0$.

What is a cubic equation?

A cubic equation is an equation of the form $ax^3 + bx^2 + cx + d = 0$, where $a$, $b$, $c$, and $d$ are real numbers and $a \neq 0$.

What is a quartic equation?

A quartic equation is an equation of the form $ax^4 + bx^3 + cx^2 + dx + e = 0$, where $a$, $b$, $c$, $d$, and $e$ are real numbers and $a \neq 0$.

What is a quintic equation?

A quintic equation is an equation of the form $ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0$, where $a$, $b$, $c$, $d$, $e$, and $f$ are real numbers and $a \neq 0$.

What is a polynomial?

A polynomial is an expression of the form $ax^n + bx^{n-1} + … + cx + d$, where $a$, $b$, $c$, …, $d$ are real numbers and $n$ is a non-negative integer.

What is a rational function?

A rational function is a function of the form $\frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials and $q(x) \neq 0$.

What is an exponential function?

An exponential function is a function of the form $

The pressure of an ideal gas is inversely proportional to its volume. This is known as:
(A) Boyle’s law
(B) Charles’s law
(C) Gay-Lussac’s law
(D) Avogadro’s law
The volume of an ideal gas is directly proportional to its temperature, if the pressure is kept constant. This is known as:
(A) Boyle’s law
(B) Charles’s law
(C) Gay-Lussac’s law
(D) Avogadro’s law
The pressure of an ideal gas is directly proportional to its temperature, if the volume is kept constant. This is known as:
(A) Boyle’s law
(B) Charles’s law
(C) Gay-Lussac’s law
(D) Avogadro’s law
The number of moles of an ideal gas is directly proportional to its volume, if the pressure and temperature are kept constant. This is known as:
(A) Boyle’s law
(B) Charles’s law
(C) Gay-Lussac’s law
(D) Avogadro’s law
The Average kinetic energy of the Molecules of an ideal gas is directly proportional to the absolute temperature of the gas. This is known as:
(A) the kinetic theory of gases
(B) the ideal gas law
(C) the first law of Thermodynamics
(D) the second law of thermodynamics
The ideal gas law is a combination of the following three laws:
(A) Boyle’s law, Charles’s law, and Gay-Lussac’s law
(B) Boyle’s law, Charles’s law, and Avogadro’s law
(C) Boyle’s law, Gay-Lussac’s law, and Avogadro’s law
(D) Charles’s law, Gay-Lussac’s law, and Avogadro’s law
The ideal gas law can be written as:
(A) $PV=nRT$
(B) $PV=nRT^2$
(C) $PV=nRT^3$
(D) $PV=nRT^4$
The molar mass of an ideal gas is the mass of one mole of the gas. It is calculated by dividing the mass of the gas by the number of moles of the gas.
(A) True
(B) False
The density of an ideal gas is the mass of the gas per unit volume. It is calculated by dividing the mass of the gas by the volume of the gas.
(A) True
(B) False
The pressure of an ideal gas is the force exerted by the gas per unit area. It is calculated by dividing the force exerted by the gas by the area of the surface over which the force is exerted.
(A) True
(B) False