# domestic electric heating Central Georgia Family Asks Community For Electric Bill Help
The cold weather means an increase in heating bills, and that can be quite expensive for several Central Georgia families. NewsCentral’s Linnie Supall spoke to one woman who reached out to the community for help.
Changes of state?

1. A 10g block of ice at 0°C is put into a glass containing 100g of water at 20°C. How much energy is taken in by the ice in melting? What will the temperature of the water be once the ice has melted? (Lf for ice = 340kJkg^-1)

2. Estimate the vertical drop of a waterfall required for a temperature difference of 0.1K between the top and the bottom

3. A shower water heater contains an electric heating element that raises the temperature of shower water from 10°C to 40°C, as it passes through the heater. If the maximum power of a domestic heater is 3.0kW, calculate the maximum rate at which the shower heater can deliver hot water. Give your answer in kgs^-1.

Thanks

(1) Lf for ice = 340 KJ/Kg = 340 J/g
So the energy is : E = m*Lf = 10*340 = 3400 J =3.4 KJ
If you want the temperature at once the ice has melted , the answer is :
t = t° – E/Mc = 20 – 3400/100*4.185 = 11.9 °C
If you want the equilibrium :
mLf + m c (te – 0) + M c (te – 20) = 0
te = (100*20 *4.185 – 3400)/110*4.185 = 10.8 °C
(2) m g h = m c deltaT
h = (c/g)*deltaT = (4185/9,81)*0.1 = 42.6 m
(3) m c (40 – 10) = 3000
c = 1 Kcal/Kg°C = 4185 J/Kg°C
m = 3000/(30*4185) = 0.024 Kg/s

Domestic for sale in Carcassonne, Languedoc-Roussillon

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