- #1
miniradman
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Homework Statement
A family uses 150 L of hot water each day. The hot water system is set to 75°C and the
supply water has a temperature of 20°C. How much energy is required? If the hot water
consumption was spread out evenly over the whole day (24 hrs), what is the total daily cost
(assuming 14 c/kWh)?
Homework Equations
[itex]Q=mC \Delta T[/itex]
[itex]C = 4.184 kJ/kg (HeatingCapacity)[/itex]
The Attempt at a Solution
Hi all, I have this question and I thought I was doing it correctly, but for some reason I'm not getting the required answer.
[itex]density of water = 998 [/itex]
[itex]Volume = 0.15 m^{3} [/itex]
[itex]m = 149.7 kg [/itex]
[itex]\Delta T = 55 [/itex]
[itex] Q=(149.7)(4.184)(55) [/itex]
[itex] Q=34424.26 kJ [/itex]
[itex] seconds/day = 86400s [/itex]
[itex] p = \frac{dQ}{dT} = \frac{\Delta Q}{\Delta T} [/itex]
[itex] p = \frac{34424.26 kJ }{86400s}[/itex]
[itex]p = 0.39843kW[/itex]
[itex]p kWh = 0.39843kW (3600)[/itex]
[itex]p kWh = 1434kWh[/itex]
[itex]cost = (0.14c) (1434kWh)[/itex]
[itex]cost = 200c = $2.00[/itex]
However the answer states that it is $1.35/day
I checked my work three times through, but I think I have a fundamental misunderstanding of something which is stopping me from getting the correct answer.