A room contains 48kg of air. How many kilowatt-hoursof energy are necessary to heat the air in the house from 9 degrees Celcius to 27 degrees Celcius? The heat capacity of air is 1.03 Jules per gram degrees Celcius.
The total heat necessary to heat up the air in the room from the initial temperature of 9 degree C to the final temperature of 27 degree C is:
`Q =m*c*Delta(T) =48000*1.03*(27-9) =889920 J`
Here the mass was taken in grams since the specific heat of air `c` is given in J/g*K.
The transformation between KWh and J is
`1KW*h =1000*3600 W*s =3.6*10^6 J`
Therefore the total energy in KWh necessary to heat up the air in the room is
`Q (KWh)= (Q(J))/(3.6*10^6) =889920/(3.6*10^6) =0.2472 KWh`
The total heat necessary to heat up the air in the room is 0.2472 KWh.