$(19$ Marks$)$ A solid block of Silver $(Ag)$ at an initial temperature of $12C$ has a mass $m_{1g}.$ It is placed with $53$ g of steam initially at $104C$ in an insulated container. The steam then condenses and becomes liquid water and the closed system reaches thermal equilibrium at a final temperature $T_f=92C.$

a$)$ By what percentage does the volume of the block of Silver increase?

b$)$ Find the heat of steam $Q_{\text{d}\text{e}\text{m}\text{a}\text{n}}$ as it condenses and becomes water at $T.$

c$)$ Calculate the heat $Q_{ig}$ gained by the block of Silver in terms of $m_{ds}.$

d$)$ Deduce the mass of the block of Silver m$/$s$.$

e$)$ Calculate the total change in entropy $AS$ of steam: first when its temperature changes from $104C$ to $100C,$ then the steam is converted into water, then water goes from $100C$ to $92C.$

f$)$ Calculate the fotal change in entropy $S$ of the whole system then prove that the Second Law of Thermodynamics is not violated.

Given: ${}_{Ag}=1\mathrm{.}75{10}^{-5}C,c_{Ag}=0\mathrm{.}0565ca\frac{l}{g}C.$

$C_{\text{s}\text{t}\text{e}\text{a}\text{m}\text{i}\text{n}}=0\mathrm{.}450ca\frac{l}{g}.C,Lv=539ca\frac{l}{g},C_{\text{n}\text{o}\text{t}\text{e}\text{r}}=1\mathrm{.}0ca\frac{l}{g}.C.$