Section A: Answer All Questions

QA$1.$ A perfectly sealed piston$-$cylinder arrangement containing $5$ moles of gas undergoes a rapid expansion at a constant temperature of $350K$ from an initial volume of $0\mathrm{.}03m^3$ to a final volume of $0\mathrm{.}04m^3.$ The expansion process takes up $6\mathrm{.}5kJ$ of heat from the surroundings and produces $3\mathrm{.}9kJ$ of work on the surroundings. The behaviour of the gas is well described by the following virial equation of state, where $B=36\mathrm{.}4c{m}^{3}mo{l}^{-1}.$

$Z=1+\frac{B}{V}$

a$)$ Calculate the internal energy and the enthalpy changes of the gas inside the cylinder during the expansion process.

$[10$ marks$]$

b$)$ Calculate the work produced if the expansion was carried out reversibly. Explain why this value is larger than the work of an irreversible expansion.

$[10$ marks$]$

QA$2.$ The inside of a house is kept at a balmy $28C$ against an average external temperature of $2C$ by action of a heat pump. At steady state, the house loses $4kW$ of heat to the outside. Inside the house, there is a large freezer that is always turned on to keep its interior compartment at $-7C,$ achieved by absorbing $2\mathrm{.}5kW$ of heat from that compartment. You can assume that both the heat pump and the freezer are operating at their maximum possible thermodynamic efficiencies. To save energy, the owner is considering:

a$)$ Increasing the temperature of the freezer to $-4C$;

b$)$ Decreasing the temperature of the inside of the house to $26C.$

Which of the two above options would be more energetically efficient $($i$.$e$.$ would save more electrical power$)?$ Justify your answer with calculations.

$[16$ marks$]$

QA$3.$ Naphthalene is a substance with a high triple point ; $P_t=1$kPa $),$ so that it sublimes at ambient conditions. Table QA$3$ shows vapour pressure data for solid naphthalene at several temperatures. Estimate the enthalpy of sublimation of naphthalene from that data, making use of an appropriate thermodynamic relation and justifying clearly any assumptions made.

$[16$ marks$]$

Table QA$3$: Vapour pressure data for naphthalene at several temperatures below the triple point.

$\backslash$table$[[$Temperature $($K$),$Pressure $($kPa$)],[350,0\mathrm{.}840],[340,0\mathrm{.}386],[330,0\mathrm{.}175],[320,0\mathrm{.}086]]$

$[$PLEASE TURN OVER$]$

CP$203/$CP$211$ Thermodynamics and Chemical Principles May $2019$ Exam

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