Final answer:
The amount of energy required to raise the temperature of a room can be calculated using the formula: Energy = Mass x Specific Heat Capacity x Change in Temperature. Given the dimensions of the room and the change in temperature.
Step-by-step explanation:
The amount of energy required to raise the temperature of a room can be calculated using the formula:
Energy = Mass x Specific Heat Capacity x Change in Temperature
We need to find the mass of the air in the room, which can be calculated using the room's dimensions and the density of air.
The density of air at room temperature and pressure is approximately 1.2 kg/m^3.
Mass of air in the room = Volume of the room x Density of air
Energy = (Mass of air in the room) x Specific Heat Capacity x Change in Temperature
Given that the dimensions of the room are 5.5m x 6.5m x 3.0m and the change in temperature is 10 degrees Celsius, we can calculate the mass of air in the room and substitute it into the formula to find the amount of energy required.
The heater's power rating of 1.5 kW can be converted to Joules per second by multiplying it by 1000, since 1 W = 1 J/s.
Calculating the required energy:
Volume of the room = (5.5m x 6.5m x 3.0m)
= 107.25 m^3
Mass of air in the room = (Volume of the room) x (Density of air) = 107.25 m^3 x 1.2 kg/m^3
= 128.7 kg
Energy = (Mass of air in the room) x Specific Heat Capacity x Change in Temperature = 128.7 kg x 21 J/K*mol x 10 degrees Celsius = 27081 J/s
= 27.081 kJ
The heater's power rating is 1.5 kW, which is equivalent to 1500 J/s. If we divide the required energy by the heater's power rating, we can find the time it will take to achieve the temperature increase:
Time = (Energy required) / (Power rating of the heater)
= 27.081 kJ / 1500 J/s
= 18.054 seconds