Q$2.$ For the remaining questions, we will assume that a heat pump will be installed to provide $60\%$ of the heat

required to heat the pool water, the reminder being provided by the solar heat exchanger. For the purposes of

the analysis below, ignore heat losses to the surroundings and do not use the COP above as that was just an

initial estimate. We will calculate the actual COP below. The operating conditions for the heat pump are:

Operates on a vapour$-$compression cycle with refrigerant R$143-$a$.$

The outlet of the compressor is at $1\mathrm{.}4$MPa and $65C.$

The outlet of the condenser is a saturated liquid at $52C.$

The inlet to the evaporator is at $10C.$

The outlet to the evaporator is at $400$kPa and $10C.$

The ambient temperature is $20C$ and the pool water temperature is to be maintained at $27C.$

Module $12$: Tutorial

a$)$ Draw the cycle numbering each stream. Start with the outlet of the evaporator as stream $1$ and number

sequentially around the cycle. Show the direction of flows and energy transfers into and out of the

system. Indicate where heat is transferred to$/$from the pool water and ambient air.

Using stream numbering as per part $($a$),$ determine:

b$)$ the flowrate of water that is recirculated through the heating system $($solar $+HP),$ knowing that the

water temperature increases by $2C.$ Assume that water has a constant heat capacity of $4\mathrm{.}18k\frac{J}{k}g.K.$

c$)$ the work required to pump the water through the heater system $($from the pool and back again$)$ if the

pressure drop for the water through the heating system in $150$kPa.

d$)$ the flowrate of refrigerant required. Q$3.$ For the heat pump in Q$2($using the same stream numbering$),$ determine:

a$)$ the compressor work.

b$)$ the flowrate of air required for the evaporator if air can only be cooled by Remember to draw your system and state your assumptions where applicable. Start with equations from the

equation and data booklet. Simplify based upon assumptions.

Q$1.$ A proposed Olympic size swimming pool is heated all year to be maintained at $27C.$ It is estimated that,

on average $($across the year$),$ the pool requires $110kW$ of heating $($yes it takes a lot of energy to heat a pool$).$

To heat the pool, water is pumped from the pool through a solar heat exchanger, then a supplementary heating

system, and back to the pool.

An average of $40\%$ of the heating will be supplied by an evacuated tube solar water heating system. For the

remaining $60\%$ of the heating required, there are three options:

A direct electric heater that is $98\%$ efficient. The $2\%$ loss is heat lost to the surroundings.

A gas fired heater that is $88\%$ efficient on the basis of the HHV of the gas. The $12\%$ loss is mostly lost

through high temperature exhaust gas with some also lost as heat to the surroundings.

A heat pump with an estimated COP of $3\mathrm{.}1$ that has the same $2\%$ heat loss to the surroundings as the

direct electric system.

Electricity costs are $$\frac{0\mathrm{.}2}{k}Wh$ and the life$-$cycle carbon intensity of the electricity is $500$kgCO$\frac{e}{M}Wh.$ Gas

costs $$\frac{0\mathrm{.}03}{M}J$ and has a life$-$cycle carbon intensity of the methane $($direct at your site and embedded

emissions$)$ is $67$kgCO$2\frac{e}{G}J.$

Determine:

a$)$ The annual MWh and GJ of electricity or gas used for each option $($i$.$e$.$ you give two numbers for each

option with different units$)$

b$)$ The annual electricity $/$ gas heating cost of each option.

c$)$ The annual $CO2e$ emissions $($in tonnes of $CO2e)$ associated with the electricity $/$ gas use for each

heating option.

d$)$ The annual $CO2e$ emissions saved $($in tonnes of $CO2e)$ by using the solar heating instead of heating

$100\%$ with each option.

e$)$ Put the results of $($a$)$ to $($d$)$ in a simple table after your calculations.

f$)$ Determine the savings, per year, of using the lowest operation cost option as compared to the highest.

Assuming the lowest operation cost option is more expensive to install and the highest operation cost

option is the cheapest, what would be an acceptable increase in initial $($capital$)$ costs if the owners

wanted a three$-$year pay back for the extra money spent initially?