Science, asked by pabdu88, 8 months ago

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

Answered by roshinik1219
0

Given:

Quantity of water in swimming pool = 15000gal\\

Initial temperature (t₁)= 63\\°F = 17\\°C

Final temperature (t₂)= 75\\°F = 24\\°C

Cost of electric energy for heating = $1$ 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= mc\\Δt\\.....(1)

where m = Mass of water

C = Specific heat of water = 4200J/kg/\\°C\\

Δt = Change in temperature = t_2-t_1

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.

1gal=3.79kg\\

Solution:

  • As per the given data, the mass (m) of water in "kg" is:1gal=3.79kg\\15000gal=15000*3.79kg\\15000gal=56850kg\\
  • The change in temperature (Δt) is calculated as follows:

        Δt= t_2-t_1

     ⇒Δt=24-17\\

     ⇒Δt=7\\°C

Now, the heat energy required is calculated using the above formula.

Q= 56850*4200*7\\Q=1671390000J\\Q=1671.39MJ\\

As per the given data, the cost of 25MJ\\ of electric energy is $1\\.

⇒The cost of 1671.39MJ is:

=(1671.39*1)/25\\=66.8556\\

Final Result:

∴ The cost of heating the pool = $ 66.8556\\.

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