Calculate the energy required in kJ to heat the water needed to fill the pool. T

Question

Calculate the energy required in kJ to heat the water needed to fill the pool. The water supply temperature is 50 degree F and a pool water temperature of 70 degree F is required. The pool dimension is 75 feet x 30 feet, with an average depth of 6 feet. Assuming no energy is lost, calculate the cost to heat this volume of water using electricity that costs 7 cents per kw-hr (current residential rates in Pullman). To properly ventilate the building, a mechanical ventilation system pushes air at a flow rate F of 17,000 m3/hr through the building and vents it outside. Calculate the total energy required to keep the inside air temperature at 80 degree F, given loss of heat from the venting air flow and loss of heat through ceiling and walls. Use an R-value of 17 for ceiling and walls and building wall dimensions of 100 ft x 50 ft x 15 ft high (ignore heat exchange with pool pool, use cp =1-01 kJ/kg degree C for specific heat of air).

Explanation / Answer

1) Energy required = Mass*C*dT

C = 4.1855 kJ/(kg-K)

Density of water 1 Kg/litre

Volume of water = length*area of trapezoid = 30*(75/2*(8+4)) = 13500 ft^3 = 382277.42 litre

T1 = 50 F = 10 C

T2 = 70 F = 21.1 C

dT = 11.1 C

Energy Required = 382277.42*1*4.1855*11.1 = 17760245.77 kJ

2) Cost of the electricity = 7 cents for 3600 kJ

Cost of the electricity to heat water = 17760245.77 / 3600 * 7 = 34533.8 cents = 345.34 dollars

Will answer 3rd question in comments below

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