20.9:
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.
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.
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 pV curve for any isothermal process is hyperbolic, since pressure is inversely proportional to volume for an ideal gas at a constant temperature.
20.9:
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,
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.
Now, the work done by an ideal gas during isothermal expansion is given by,
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.
Suggested Reading
- Young, H. D, and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson. pp 635.
- OpenStax. (2019). University Physics Vol. 2. [Web version]. pp 121 Retrieved from https://openstax.org/books/college-physics/pages/15-2-the-first-law-of-thermodynamics-and-some-simple-processes