Applications
Isothermal processes can occur in any kind of system, including highly-structured machines, and even living cells. Various parts of the cycles of some heat engines are carried out isothermally and may be approximated by a Carnot cycle. Phase changes, such as melting or evaporation, are also isothermal processes.
In Isothermal non flow Process, the work done by compressing the perfect gas (Pure Substance) is a negative work, as work is done on the system, as result of compression, the volume will decrease, and temperature will try to increase. To maintain the temperature at constant value (as the process is isothermal) heat energy has to leave the system and enter the environment. The amount of energy entering the environment is equal to the work done (by compressing the perfect gas) because internal energy does not change. The thermodynamic sign convention is that heat entering the environment is also negative. Thence Q = W.
In equation of work, the term nRT can be replaced by PV of any state of an ideal gas. The product of pressure and volume is in fact, 'Moving Boundary Work'; the systems boundaries are compressed. For Expansion the same theory is applied.
As per Joule's Law for the perfect gas, Internal energy is the function of absolute temperature. In an Isothermal process the temperature is constant. Hence, the internal energy is constant, and the net change in internal energy is ZERO. Within the perfect, or ideal gas, there are no inter-molecular forces and the gas particles are infinitesimal. However, for a real pure substance there is a component of internal energy corresponding to the energy used in overcoming inter-molecular forces. In an Isothermal process, when the volume of the gas changes, the average distance between each molecule changes as well. So if the real pure gas undergoes an Isothermal process, there is a net change in internal temperature consistent with this component of internal energy.
Read more about this topic: Isothermal Process