Reversible processes of an ideal gas

We will apply the first law of Thermodynamics to calculate the work, the heat exchanged and the change in the internal energy for the four most usual reversible processes that an ideal gas can undergo: isothermal, isochoric, isobaric and adiabatic.

In all cases, we will use Clausius’ convention to state the first law of Thermodynamics:

Where W is the work done by the system on its surroundings.

Sign convention: 

  • The work done by a gas on its surroundings is positive when it expands. When the gas compresses, the work done is negative.
  • The heat consumed by a system is positive. The heat supplied by a system to its surroundings is negative.

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All temperatures will be expressed in kelvin and we will use SI units (pressure in pascal and volume in m3). In SI units, the ideal gas constant is:

We will use n moles of an ideal gas enclosed in a container like the one shown in the figure below to study the four processes.

We will use a PV diagram to represent the different states and the processes that gas undergoes.

Click on the following links to see the details for the different processes.

Follow the links below to see how to calculate the work, heat and the change in the internal energy for the following four reversible processes undergone by an ideal gas:

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Summary table

Follow the links to see how the quantities shown in the summary table are calculated.

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