During 4 hours one winter afternoon, when the outside temperature was 10° C, a house heated by electricity was kept at 19° 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)? watts (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 22° C (71.6° F), how many kwh of electricity would have been consumed? kwh

a

The average energy leakage is  

b

The KWh of electricity consumed is  

Explanation:

From the question we are told that

      The temperature outside C

       The The duration is  

       The Annual energy expenditure is  

        The temperature of the house is

The average energy leakage(A) can be mathematically obtained by this formula

Given that the house temperature

  The electrical energy consumed at is

   The electrical energy consumed at is

Since energy is proportional to

Where is the temperature of outside ()

The expression of the relationship between E and is mathematically represented as

Substituting values

 Now making the subject of the equation