Water has a specific heat capacity of 4186 J/kg $^{\circ}$C.A tank contains 500 kg of water at 10.0$^{\circ}$C.The water is heated up to a temperature of 90.0$^{\circ}$C.If electricity costs $0.100 per kilowatt-hour,then what is the cost of heating the water?

Question

Quizplus · Accepted Answer

First, we need to find the amount of energy needed to heat up the water:
Q = m * c * ΔT
where
m = 500 kg (mass of water)
c = 4186 J/kg·°C (specific heat capacity of water)
ΔT = 90°C - 10°C = 80°C

Q = 500 kg * 4186 J/kg·°C * 80°C
Q = 16,744,000 J or 16.74 MJ

Next, we need to convert MJ to kWh:
1 kWh = 3.6 MJ
16.74 MJ / 3.6 MJ/kWh ≈ 4.65 kWh

Finally, we can calculate the cost of electricity:
4.65 kWh * $0.100/kWh = $0.465 or $4.65

Therefore, the best choice is C.

Water Has a Specific Heat Capacity of 4186 J/kg ∘^{\circ}∘ CA Tank Contains 500 Kg of Water at 10

Water Has a Specific Heat Capacity of 4186 J/kg $^{\circ}$ CA Tank Contains 500 Kg of Water at 10