A well$-$insulated vessel contains $3$ kg of liquid propane at $50\backslash$deg C and $1$ bar pressure. A $10$ kg mass

of steel at a temperature of $150\backslash$deg C is immersed in the propane. Heat is transferred from the steel to

the propane until they reach thermal equilibrium. Assuming that this process occurs at constant

pressure, determine:

a$)$ the final temperature $(\backslash$deg C$)$; $[2$ marks$]$

b$)$ the final quality of the propane; $[4$ marks$]$

c$)$ the amount of heat transferred $($kJ$)$ between the steel and the propane; $[2$ marks$]$

d$)$ the work done $($kJ$)$ by the propane on the surroundings during the process; $[4$ marks$]$

e$)$ the total entropy production during the process $($kJ$/$K$).[4$ marks$]$

Data: Specific heat capacity of steel $=0\mathrm{.}48$ kJ kg$1$ K$1$

a$)42\mathrm{.}38$ deg C

b$)68\mathrm{.}3\%$

c$)85\mathrm{.}4$ kJ

d$)1\mathrm{.}10$ kJ$/$K