When a system contains regions that differ in physical structure or chemical composition,

an overall value can be assigned to its properties. Consider the system, $$System $1,$ shown

below $($note that $$a$$ and $$b$$ can be considered to be touching in System $1).$ It contains na

molecules in state $$a$$ and nb molecules in state $$b$.$

a$.$ Develop an expression for the extensive volume V$1$ of System $1$ in terms of na$,$ nb$,$

and the volumes of each homogeneous region Va and Vb$.$

b$.$ Develop an expression for the intensive molar volume vm$,1$ in terms of na$,$ nb$,$ and

the molar volumes of each homogeneous region vm$,$a and vm$,$b$.$

c$.$ Generalize the result of $($a$)$ to come up with an expression for any extensive

property K$1$ in terms of na$,$ nb$,$ and the extensive properties Ka and Kb$.$

d$.$ Generalize the result of $($b$)$ to come up with an expression for any intensive property

km$,1$ in terms of na$,$ nb$,$ and the intensive properties km$,$a and km$,$b$.$

$3.$ Consider a rigid, thick$-$walled tube that is filled with H$2$O liquid and vapor at $0\mathrm{.}2$ MPa.

After it is sealed, it is heated so that it passes through its critical point. What fraction of the

mass in the tube is vapor in the initial state?

$4.$ What size vessel holds $2$ kg water at $80$C such that $70\%$ is vapor? What are the pressure

and enthalpy $($H$)?$ Note: although we have not talked extensively about enthalpy in class,

you may simply look up values of H on the steam tables for this and related problems on

this assignment.

$5.$ Determine the temperature, quality, and internal energy $($U$)$ of $4$ kg of water in a rigid

container of volume $1$ m$3$ at a pressure of $1\mathrm{.}6$ bar.

$6.$ Three kg of saturated liquid water are evaporated at $60$C$.$

a$.$ At what pressure will this occur at equilibrium?

b$.$ What is the initial volume?