Question

A backyard swimming pool is 12 feet in diameter and 36 inches

deep. It is filled with water from a hose at 8.0 degrees celcius.

Determine the amount of heat that must be added to the water to

raise the temperature to 28 degrees celcius. The specific heat

capacity of water is 4186 J/kg/C.

Answer 1

d = 12 feet

h = 36 inches = 3 feet

Initial temperature:

$t_i= 8 \;°C \\ V_{water}= \frac{\pi d^2h}{4} \\ = \frac{\pi \times 12^2 \times 3}{4} \\ = 34.377 \;ft^3 \\ = 0.9734 \;m^3$

Mass of water $= Volume \times Density$

$= 0.9734 \times 1000 \\ = 973.4 \;kg$

Final temperature

$t_f = 28 \;°C \\ Q=mcΔT \\ = 973.4 \times 4186 \times (28-8) \\ = 81493047 \;J \\ = 81.5 \; MJ$