Name: isothermal expansion and heat transfer
Uploaded: 2025-08-19T15:10:28.000Z
Duration: 1 min 21 s
Channel: JoVE

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Isothermal Processes

A thermodynamic process that occurs at a constant temperature is called an isothermal process.Conversion of boiling water into steam at a constant temperature of 100 degrees Celsius is an example of an isothermal process. Similarly, the conversion of water into ice at 0 degrees Celsius is also an isothermal process.Now, consider an ideal gas system enclosed in a sealed gas syringe at a constant temperature.When the plunger is slowly pushed in a controlled manner, the gas inside the syringe is compressed. The reduced volume of the gas causes an increase in pressure; however, the temperature remains constant.Releasing the plunger in a controlled manner leads to an expansion of the gas at constant temperature.The change in internal energy is zero for these processes as the temperature does not change. Thus, using the first law of thermodynamics, the work done equals heat.The pV curve for any isothermal process is hyperbolic, since pressure is inversely proportional to volume for an ideal gas at a constant temperature.

isothermal processes

A thermodynamic process that occurs at constant temperature is called an isothermal process. Heat slowly flows into the system or out of the system to maintain thermal equilibrium. Processes involving phase changes like water evaporation into steam or freezing water into ice at a constant temperature are examples of Isothermal Processes.
An ideal gas can also undergo isothermal expansion or compression.
For example, consider 1 mole of an ideal gas inside an isolated cylinder at initial volume V and pressure p. Suppose the heat added to the system causes a quasistatic expansion of the gas at a constant temperature of 300 K. If the volume of the gas changes to 2V, what is the amount of heat added to the system?
Here the known quantities are the number of moles of the gas, initial and final volume of the gas. The unknown quantity, heat, is to be calculated.
According to the first law of thermodynamics,
<img alt="Thermodynamics first law equation &#916;U=Q&#8722;W, energy conservation principle, scientific concept" src="/files/ftp_upload/13682/13682_Equation_PT_1.svg" style="text-align: center; height: 13px;" data-altupdatedat="1761830439000" data-alt="Equation1" />
As the temperature is constant, the change in internal energy for this process is zero. Thus, the heat added to the system equals the work done by the system.
<img alt="Q=W equation, thermodynamics concept, energy work relation, educational formula illustration" src="/files/ftp_upload/13682/13682_Equation_PT_2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1761830439000" data-alt="Equation2" />
Now, the work done by an ideal gas during isothermal expansion is given by,
<img alt="Thermodynamics equation W=nRTln(V2/V1) work calculation formula." src="/files/ftp_upload/13682/13682_Equation_PT_3.svg" style="text-align: center; height: 32px;" data-altupdatedat="1761830439000" data-alt="Equation3" />
Substituting for the number of moles, gas constant, temperature, initial volume, and the final volume of the gas, the work done is equal to 1728.85 J.
Since the work done by the system equals the heat added to the system, it is considered that 1728.85 J of heat is applied to the system to expand it isothermally to 2V.

A thermodynamic process that occurs at constant temperature is called an isothermal process. Heat slowly flows into the system or out of the system to ...

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The First Law of Thermodynamics

KEY TERMS AND CONCEPTS

isothermal expansion and heat transfer

An isothermal process is a thermodynamic process that happens at constant temperature. During the process, heat slowly flows into the system or out of the system so thermal equilibrium is maintained.

Phase changes are common examples of isothermal processes. Water can evaporate into steam at a constant temperature, and water can also freeze into ice at a constant temperature. An ideal gas can also undergo isothermal expansion or compression.

Here, an ideal gas in an isolated cylinder expands quasistatically at 300 K. The gas starts with 1 mole at volume V and pressure p. The volume then changes to 2V, and the heat added to the system must be found.

By the first law of thermodynamics, the change in internal energy is zero because the temperature stays constant. That means the heat added to the system equals the work done by the system. For an ideal gas in isothermal expansion, the work is calculated from the initial and final volume.

Substituting the number of moles, gas constant, temperature, and volumes gives a work value of 1728.85 J. Since the work done by the gas equals the heat added, 1728.85 J of heat is applied to expand the gas isothermally to 2V.

Isothermal Expansion and Heat Transfer

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Learn how isothermal processes keep temperature constant while heat equals work during ideal gas expansion, with phase change and cylinder examples.

Isothermal Expansion and Heat Transfer | JoVE K12

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Isothermal Expansion and Heat Transfer

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