Module 2 : Phase Transitions

Lecture 6 : Stable Equilibrium

Example 6

Two particular systems have the following equations of state

where , and the subscripts indicate systems 1 and 2. The mole number of the first system is N1 = 0.4, and that of the second is N2 = 0.8. the two systems are contained in a closed adiabatic cylinder, separated by a movable diathermal piston. The initial temperatures are T1 = 400 K and T2 = 800 K, and the total volume is 0.1 m3 . what is the energy and volume of each system in equilibrium? What is the pressure and temperature?

Solution

Let the subscript for initial and final parameters be denoted by i-j and f-j where j indicates the subsystem 1 or 2.
Let Tf be the final temperature of the whole system (taking both the subsystems together)