During 4 hours one winter afternoon, when the outside temperature was 11° C, a house heated by electricity was kept at 24° C with the expenditure of 58 kwh (kilowatt·hours) of electric energy.

(a) What was the average energy leakage in joules per second (watts) through the walls of the house to the environment (the outside air and ground)?

(b) The rate at which energy is transferred between two systems due to a temperature difference is often proportional to their temperature difference. Assuming this to hold in this case, if the house temperature had been kept at 27° C (80.6° F), how many kwh of electricity would have been consumed?

a. The average energy leakage in joules per second (watts) = 14500J/s

b. The number of kwh of electricity would have been consumed = 62.25kwh

Explanation:

a.

Given that the house maintains a constant temperature.

The meaning of this is that all energy entering the house must be leaked through the walls of the house because if it didn't leak through the walls, some energy will be stored in the house and this will increase the temperature of the house.

The relationship between the above is

P = E/t

Where E = 58kwh

And t = 4 hours

P = 58/4

P = 14.5

P = 14.5 * 1000J/s

P = 14500J/s

b.

Given that the rate at which energy is transferred between two systems due to a temperature difference is often proportional to their temperature difference.

This can be represented as follows;

P = k∆T --- make I the subject of formula

k = P/∆T

k = P1/∆T1 = P2/∆T2

Make P2 the subject of formula

P2 = (P1 * ∆T2)/∆T1

Where P1 = 14500J/s

∆T2 = 27 - 0 = 27°C

∆T1 = 24 - 0 = 24°C

So,

P2 = 14500 * 27 / 24

P2 = 16,312.5J/s

The number of kwh of electricity would have been consumed = 16,312.5 * 4

The number of kwh of electricity would have been consumed = 65,250Wh

The number of kwh of electricity would have been consumed = 62.25kwh

the correct choice is a .

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