Question $4$:

$($a$)$ Give the Kelvin$-$Plank statement of the $2$nd Law of Thermodynamics. Based on this

statement, why must the thermal efficiency of any heat engine be less than unity?

$[5$ Marks$]$

$($b$)$ A container containing $1000$ kg of liquid water initially at $80\backslash$deg C is brought into a room. The

$4$m x $5$m x $7$m room is well insulated and sealed, and initially at a temperature of $22$oC$.$

Answer the following:

$($i$)$ What is the final temperature of the water and the total amount of energy

transferred from the water to the air? $(10$ Marks$)$

$($ii$)$ What is the entropy change of the water? $(4$ Marks$)$

$($iii$)$ Despite the entropy change of the water being calculated as negative in Part $($ii$)$

of this question, show that this does not violate the Increase in Entropy Principle.

$(6$ Marks$).$

$($Note: In your solution, you can assume the specific heat of water is constant at $4\mathrm{.}18$ kJ$/$kgK$)$