Thermodynamic Changes in Expansion Processes

Isothermal. As pointed out in Equation (3.6), work performed in a finite gaseous expansion is given by the expression 

Any finite expansion that occurs in a finite time is irreversible. A reversible expansion can be approximated as closely as desired, and the values of the thermodynamic changes can be calculated for the limiting case of a reversible process. In the limiting case, the process must be carried out infinitely slowly so that the pressure P is always a well-defined quantity. A reversible process is a succession of states, each of which is an equilibrium state, in which the temperature and pressure have well-defined values such a process is also called a quasi-static process. 

As the actual work done approaches the reversible work, the pressure P of the gas and the external pressure P differ infinitesimally, and the direction of change can be 

Because the reversible process is a succession of equilibrium states, P is given by the equation of state, which is Equation (5.1) for an ideal gas. Substituting from Equation (5.1) into Equation (5.19), we obtain 

With this information and the use of the first law of thermodynamics, we can calculate the heat absorbed from the surroundings in the process  

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