If a person was locked in a perfectly insulated room 8ft by 8ft by 10ft, how long would it take the room temperature to increase from 75 degree Farenheit to 100 degree Farenheit? The density of air is 1.2 Kg/Cubic meter and 1 watt sec is its specific heat. A person's body heat output is 100 watts and their volume is 3 cubic feet.
To find the time it would take for the room temperature to increase from 75°F to 100°F, we need to consider the heat transfer occurring within the room.
First, let's calculate the volume of the room in cubic meters:
8 ft x 8 ft x 10 ft = 640 cubic feet
1 cubic foot is equal to approximately 0.0283 cubic meters, so:
640 cubic feet x 0.0283 cubic meters = 18.112 cubic meters
Next, we calculate the mass of air in the room:
Density of air = 1.2 kg/cubic meter
Mass of air = Density x Volume
Mass of air = 1.2 kg/cubic meter x 18.112 cubic meters ≈ 21.7344 kg
Now, let's determine the amount of heat that needs to be transferred to the room to increase its temperature.
The specific heat capacity of air is given as 1 watt-sec. This means that it takes 1 watt of energy to heat 1 kilogram of air by 1 degree Celsius.
In this case, we want to increase the temperature from 75°F to 100°F, which is a difference of 25°F. We need to convert this to Celsius:
(100°F - 32) x 5/9 = 37.8°C
(75°F - 32) x 5/9 = 23.9°C
Temperature difference = 37.8°C - 23.9°C = 13.9°C
To convert the Celsius temperature difference to Kelvin, add 273.15:
Temperature difference = 13.9°C + 273.15 = 287.05 K
Now, we can calculate the heat energy needed:
Heat energy = Mass x Specific heat capacity x Temperature difference
Heat energy = 21.7344 kg x 1 watt-sec/kg x 287.05 K ≈ 6264.18 watt-sec
To find the time it takes to transfer this amount of heat, we need to consider the heat output of the person in the room.
The person's heat output is given as 100 watts. We'll assume that all the heat generated by the person is transferred to the air in the room.
Finally, we can calculate the time it takes to heat the room by dividing the heat energy needed by the heat output of the person:
Time = Heat energy / Heat output
Time = 6264.18 watt-sec / 100 watts ≈ 62.64 seconds
Therefore, it would take approximately 62.64 seconds to increase the room temperature from 75°F to 100°F, assuming all the heat generated by the person is transferred to the air in the room.