Question

a) An electric water heater holds 209 L. If electricity costs 0.19 $ per kWh, how much does it cost to raise the water temperature from 10 ?C to 65 ?C? Express your answer to two significant figures and include the appropriate units.

b)How much energy is required to melt a 160 g copper cube initially at 948 ?C? Express your answer with the appropriate units.

Answer 1

Energy required to raise the temperature of water will be given by:

Q = m*C*dT

m = mass of water = volume*density = 0.209 m^3*1000 kg/m^3

m = 209 kg

C = Specific heat of water = 4186 J/kg-C

dT = 65 - 10 = 55

So

Q = 209*4186*55

Q = 4.812*10^7 J

Power is given by:

P = Q/t

1 J = 1 W-sec

Q = P*t

Q = 4.812*10^2 W-sec = 13366.67 W-hr = 13.367 kWh

Price of 1 kWh = $0.19

Total price = 13.367*0.19 = $2.54

Part B

Energy required to melt copper will be

Q = Q1 + Q2

Q1 = energy required to raise temperature from 948 C to melting point = m*C*dT

Q2 = energy required to melt the copper = m*Lf

Lf = latent heat of fusion = 209 kJ/kg

C = specific heat of copper = 386 J/kg-C

m = mass of copper = 160 gm = 0.16 kg

dT = 1085 - 948 = 137 C

So,

Q = 0.16*386*137 + 0.16*209*10^3 = 41901 J

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