What is the cost, in dollars, of heating the hot tub, assuming 75.0% efficiency to account for heat transfer to the surroundings?

$ 5.93

Explanation:

If we are to put into consideration the following factors even though it was not all stated in the question.

What is the cost of heating a hot tub containing 1500 kg of water from 10.0°C to 40.0°C, assuming 75.0% efficiency to take heat loss to surroundings into account? The cost of electricity is ¢8.50/kW·h.

Q = mc∆T 1

Where m is the mass of water = 1500kg

C is the specific heat capacity of water = 4.184

∆T = temperature change

= 40° - 10°

= 30°

Now, substitute the values into equation 1

= 1500×4.184×30

= 188280

Q in kw/s

= 188280/3600

= 52.3kw/hr

Efficiency = 75%

= 75/100

= 0.75

Hence we have

52.3/0.75

= 69.73kw/hr

C = Q × cost per kw/hr

C = 69.73× $8.5/100

C = 5.92705

C =$ 5.93

Hence, the cost of heating the hot tub is $ 5.93

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