Question $1$

$($a$)$ Sketch a $p-T$ diagram $($phase diagram$)$ for a pure substance that contracts on freezing. Show and label the phase change lines, the critical and the triple points, and label the three phase regions.

$($b$)$ Use the steam tables to find the specific volume of steam at $200$ kPa and $300C.$ Then show that the error in assuming steam is an ideal gas under these conditions is less than $0\mathrm{.}5\%.$

$($c$)$ Briefly explain what is meant when a substance is described as a compressed liquid. Explain also why a sub$-$cooled liquid is the same as a compressed liquid.

$($d$)$ A $2$ kg block of copper undergoes a temperature change from $20C$ to $34C.$ Determine the entropy change of the block.

$($e$)$ A refrigeration unit rejects $6\mathrm{.}3$ kW of heat into a room at $30C$ while keeping a freezer cabinet at a temperature of $-21C.$ If the COP for the refrigeration unit under these circumstances is $2\mathrm{.}4$ then determine:

$($i$)$ The heat removed from the freezer cabinet and the power required to drive the refrigeration unit.

$($ii$)$ The power required to drive the refrigeration unit under ideal, reversible operation for the same temperatures and amount of heat removed from the freezer cabinet.

$($f$)$ For a real $($irreversible$)$ process from state $1$ to state $2$ in a closed system it is found that the entropy does not change $($i$.$e$.S_2-S_1=0).$ With reference to the terms on the right$-$hand side of the following

equation briefly explain why there must be a heat loss in this process.

$S_2-S_1={\displaystyle \underset{1}{\overset{2}{}}}(\frac{Q}{T})+S_{\text{g}\text{e}\text{n}}$

have answers but need working.