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Thermodynamics fill in the blanks The swimming pool at the local YMCA holds roughly 749511.5 L (749511.5 kg) of water and is kept at a temperature of 80.6 °F year round using a natural gas heater. If you were to completely drain the pool and refill the pool with 50°F water, (blank) GJ (giga-Joules) of energy are required to to heat the water back to 80.6 °F. Note: The specific heat capacity of water is 4182 J/kg ⋅°C. The cost of natural gas per GJ is $2.844. It costs $ (blank) to heat the pool (to the nearest dollar).

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Answer:

[tex]95.914\ \text{GJ}[/tex]

[tex]\$272.78[/tex]

Explanation:

m = Mass of water = 749511.5 kg

c = Specific heat of water = 4182 J/kg ⋅°C

[tex]\Delta T[/tex] = Change in temperature = [tex]80.6-50=30.6^{\circ}\text{F}[/tex]

Cost of 1 GJ of energy = $2.844

Heat required is given by

[tex]Q=mc\Delta T\\\Rightarrow Q=749511.5\times 4182\times 30.6\\\Rightarrow Q=95.914\times 10^9\ \text{J}=95.914\ \text{GJ}[/tex]

Amount of heat required to heat the water is [tex]95.914\ \text{GJ}[/tex].

Cost of heating the water is

[tex]95.914\times 2.844=\$272.78[/tex]

Cost of heating the water to the required temperature is [tex]\$272.78[/tex].