In a tank of steam at $2\mathrm{.}068$ bar and $477\mathrm{.}6K,$ the Keenan and Keyes steam tables show

that the entropy is $7\mathrm{.}510\frac{J}{g}K.$ The reference entropy is $0\mathrm{.}0$ for saturated liquid water at

$273\mathrm{.}2K.$ Suppose that you had a tank of steam at $2\mathrm{.}068$ bar and $477\mathrm{.}6K$ that contained

$10g$ of steam. You now injected a small quantity of additional steam $($at $2\mathrm{.}068$ bar and

$477,6K)$ into the tank under conditions that the total entropy and pressure remained

constant. The value of $C_p$ for steam at $2\mathrm{.}068$ bar and $477\mathrm{.}6K$ is about $2\mathrm{.}01\frac{J}{g}K.$

$($a$)$ Derive a general expression for the temperature change per role of component $j$

added to a multicomponent mixture in which the total entropy, pressure, and moles

of all components $($other than $j)$ are maintained constant.

$($b$)$ Estimate the initial temperature change $(\frac{K}{?}$ per gram of steam$).$ What would this

derivative had been if$,$ with a different reference state for entropy, we had chosen

$S=0$ for superheated steam, $P=\frac{2\mathrm{.}068}{b}ar,T=477\mathrm{.}6K?$ How do you reconcile

your answers?