MASSACHUSETTS INSTITUTE OF TECHNOLOGY

Thermodynamics of Materials

3.00 Fall 2000

W. Craig Carter

Department of Materials Science and Engineering

Massachusetts Institute of Technology

77 Massachusetts Ave.

Cambridge, MA 02139

Problem Set 8: Due Fri. Dec. 1, Before 5PM in 13-5049

Exercise 8.1

Consider the single component phase diagram:

Figure 8-1-i: Single component phase diagram.

1. Write down the differential equation for each one of the curves in the $P$-$T$ plane in terms of the molar entropies and volumes of the liquid, solid, and vapor phases ( $\ensuremath{\overline{\ensuremath{{S}^{\mbox{liquid}}}}}$, $\ensuremath{\overline{\ensuremath{{S}^{\mbox{solid}}}}}$, $\ensuremath{\overline{\ensuremath{{S}^{\mbox{vapor}}}}}$, $\ensuremath{\overline{\ensuremath{{V}^{\mbox{liquid}}}}}$, $\ensuremath{\overline{\ensuremath{{V}^{\mbox{solid}}}}}$, $\ensuremath{\overline{\ensuremath{{V}^{\mbox{vapor}}}}}$ )

2. Instead of the $P$-$T$ plane in the figure above, make a sketch of the phase diagram for one mole of the same material in the $\ensuremath{{V}^{\mbox{total}}}$- $\ensuremath{{S}^{\mbox{total}}}$ plane.