How many kilowatt-hours of energy are necessary to heat the air in the house from 9∘C to 30∘C? The heat capacity of air is 1.03 J/g∘C.A room contains 45kg of air.
q needed to heat the air is
q = mass air x specific heat air x (Tfinal-Tinitial)
Then 1 watt*s = J
Convert J to watt and then to kW and kW-hr.
0.30 kW-hr
To calculate the number of kilowatt-hours (kWh) required to heat the air in the house, we need to follow these steps:
Step 1: Find the temperature difference
The temperature difference is the change in temperature. In this case, it is the difference between the final temperature (30°C) and the initial temperature (9°C):
Temperature difference = Final temperature - Initial temperature = 30°C - 9°C = 21°C
Step 2: Calculate the energy required
The energy required to heat the air can be calculated using the formula:
Energy (E) = mass (m) × specific heat capacity (c) × temperature difference
Given:
Mass (m) = 45 kg
Specific heat capacity (c) = 1.03 J/g°C (Note: We need to convert it to J/kg°C)
Since the specific heat capacity is provided in grams, we need to convert it to kilograms:
Specific heat capacity (c) = 1.03 J/g°C × (1 kg / 1000 g) = 0.00103 J/kg°C
Now, we can calculate the energy required:
Energy (E) = 45 kg × 0.00103 J/kg°C × 21°C
Step 3: Convert energy to kilowatt-hours (kWh)
We need to convert the energy from joules (J) to kilowatt-hours (kWh):
1 kWh = 3.6 × 10^6 J (1 kilowatt-hour is equal to 3.6 million joules)
Energy (E) in kilowatt-hours (kWh) = (45 kg × 0.00103 J/kg°C × 21°C) / (3.6 × 10^6 J/kWh)
Performing the calculation, we get:
Energy (E) ≈ 0.0010625 kWh
Therefore, approximately 0.0010625 kilowatt-hours (kWh) of energy are required to heat the air in the house from 9°C to 30°C.