An average residential swimming pool contains
about 15,000 gal. Suppose the owner wants to use an elec-
tric pool heater to heat the water in such a pool from 63°F
(about 17°C) to 75°F (24°C). If electric energy costs about $1
per 25 MJ, about how much will this cost?
Answers
Given:
Quantity of water in swimming pool =
Initial temperature (t₁)= °F = °C
Final temperature (t₂)= °F = °C
Cost of electric energy for heating = $ per 25MJ
To find:
The cost of heating the pool as per the requirements of the owner.
Formula to be used:
Heat energy required to raise the temperature of water from t₁ to t₂ is given by:
Heat energy= Δ.....(1)
where m = Mass of water
C = Specific heat of water = °
Δt = Change in temperature =
To be recollected:
Specific Heat: Specific heat is defined as the heat required to rise the temperature of any substance of mass 1gram by a temperature of 1°C.
Given quantity of water is in gallons. It should be converted into "kg", for the calculation.
Solution:
- As per the given data, the mass (m) of water in "kg" is:
- The change in temperature (Δt) is calculated as follows:
Δ
⇒Δ
⇒Δ°C
Now, the heat energy required is calculated using the above formula.
As per the given data, the cost of of electric energy is $.
⇒The cost of 1671.39MJ is:
Final Result:
∴ The cost of heating the pool = $ .