In an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 12.0C. The temperature at the inside surface of the wall is 22.0C. The wall is 0.10m thick and has an area of 10.0m^2. Assume the one kilowatt*hour of electrical energy costs $0.10. How many hours are required for one dollar's worth of energy to be conducted through the wall?
The heat conducted for a time t is given by,
Q= (k*A*delta T)t/L
Q=the heat conducted
t=time = 1 hour = 3600s (if used for one hour)
L=length of bar = 0.1m is the thickness of the concrete
A=cross-sectional area = 10 m^2
delta T=temperature difference between the ends of the bar
= 22-12 = 10C
This solution is provided in 269 words. It gives the equation for heat conducted for time and uses the kilowatt-hour of energy to find total electrical energy costs.