Question

A room contains 49 kg of air. How many kilowatt-hours of energy are necessary to heat the air in the house from 5 ∘C to 30 ∘C? The heat capacity of air is 1.03 J/g∘C.

Express your answer using two significant figures.

Answer 1

given

49 kg of air

heat capacity of air is 1.03 J/g∘C

initial temperature = 5^∘C

Final temperature = 30^∘C

we know that

q = m s T

m is mass

s is heat capacity

T is change in temperature

so

q = 49 * 1000 g * 1.03 J/g∘C * (30-5)^∘C

= 1261750 J

now

1 J = 2.8 * 10^-7 kilowatt-hours

so

1261750 J = 1261750 J * 2.8 * 10^-7 kilowatt-hours / J

= 0.35 kilowatt-hours