Before leaving for a vacation£¬the owners of a home 8.0m *21m*5.0m turn the thermostat down to 14celcius. On their return£¬how much heat is needed to raise the temperature of the air inside the home to 21celcius£¿Ignore the heat needed to warm the walls and the contents of the house.The density of air is 1.3kg/m3.
To find the amount of heat needed to raise the temperature of the air inside the home, we can use the formula:
Q = m * c * ΔT
Where:
Q is the amount of heat in joules,
m is the mass of the air,
c is the specific heat capacity of air,
ΔT is the change in temperature.
To calculate the mass of the air, we need to find the volume of the home. The volume of the home can be calculated by multiplying its dimensions:
Volume = length * width * height
= 8.0m * 21m * 5.0m
= 840 cubic meters
Now, we can calculate the mass of the air:
Mass = density * volume
= 1.3kg/m^3 * 840m^3
= 1092 kg
The specific heat capacity of air is approximately 1005 joules per kilogram per degree Celsius.
Now, we can calculate the change in temperature:
ΔT = final temperature - initial temperature
= 21°C - 14°C
= 7°C
Finally, we can calculate the amount of heat needed:
Q = m * c * ΔT
= 1092kg * 1005 J/(kg·°C) * 7°C
≈ 7,661,740 joules
Therefore, approximately 7,661,740 joules of heat are needed to raise the temperature of the air inside the home from 14°C to 21°C.