A reversible isothermal process is a reversible thermodynamic process that occurs at constant temperature.
A reversible isothermal expansion process for an ideal gas follows the path from A to C, while a reversible isothermal compression moves from C to A (see diagram above). The curve that describes an isothermal process is called an isotherm. We can express work done for a reversible isothermal process, which involves the change in pressure and volume of the system, by substituting the ideal gas law in eq5 to give:
To determine the work done on a system undergoing reversible isothermal expansion or compression, we immerse the piston-cylinder device in a constant temperature water bath. For a reversible isothermal compression, the external force balances the force exerted by the gas on the underside of the piston before the system is compressed. At the start of the compression, the external force is increased infinitesimally causing the piston to move down over an infinitesimal distance.
Consequently, infinitesimal energy is transferred via work to the system, leading to an infinitesimal increase in the kinetic energy of the gas and hence, an increase in the system’s temperature. The infinitesimal difference in temperature between the system and the water bath results in the flow of energy from the system through the thermally conducting cylinder walls to the temperature controlled water bath. Hence, constant temperature of the system is maintained throughout the process. This compression process is repeated stepwise with further infinitesimal increases in the external force until the desired final volume of the system is achieved. Work done is then calculated using eq6. If the external force is now decreased infinitesimally in a stepwise manner, we have a reversible isothermal expansion of the gas. Many chemical reactions involving the determination of rates of reactions are carried out isothermally.
Question
Does the temperature of the water bath increase if energy is continuously transferred from the system to the water bath in the compression process?
Answer
Theoretically, the constant temperature water bath is infinitely large. This means that transfer of energy from the system to the layer of water in the vicinity of the system (due to a temperature difference between the two) is the first of infinite steps of transfer, with the second step being the transfer of energy from the body of water in the vicinity of the system to a layer of water further away from the system and so on. In practice, the temperature of the water bath is controlled by a computer and adjusted throughout the process to maintain constant temperature for the system.
