Isothermal Lines

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


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