Helmholtz free energy near a phase transition
Consider a material described by the phase diagram shown below. A quantity of this material is placed in a cylinder that is in contact with a thermal reservoir at temperature Ta. The temperature is held constant, and the pressure is increased as shown on the phase diagram, through the point b (on the coexistence curve) to the point c.
1. Make a qualitative sketch of the pressure P as a function of volume V during the process that takes the system from the state a, through the state b, to the state c. Label the points on the phase diagram corresponding to states a, b, and c. Label the phases. Explain the signs and relative magnitudes of the slopes of the lines you draw. Explain any discontinuities in the function or its slope.
2. Sketch the Helmholtz free energy F as a function of the volume V for this process. Again label the phases and the points corresponding to states a, b, and c. Explain the relative magnitudes of the slopes and curvatures of the lines you draw. Explain any discontinuities in the function or its slope.