A glass window 5ft by 8 ft 0.3 in whose inner and outer faces are at respective temperature of 65°F and 64°F.The thermal conductivity of glass is 5.5 BTU over ft squared x hr x°F over inches
Find its:
A.)temperature gradient
B.)Resistance
C.)Driving force
D.)Heat conducted in BTU per day
To find the temperature gradient, we need to calculate the temperature difference between the inner and outer faces of the glass window.
Temperature gradient = Temperature difference / Thickness
First, let's convert the thickness of the window to feet:
0.3 in = 0.3/12 ft = 0.025 ft
Now, calculate the temperature difference:
Temperature difference = Inner face temperature - Outer face temperature
= 65°F - 64°F
= 1°F
Substitute the values into the temperature gradient formula:
Temperature gradient = 1°F / 0.025 ft
= 40°F/ft
Therefore, the temperature gradient is 40°F/ft.
To find the resistance, we need to use the formula:
Resistance = Thickness / (Thermal conductivity * Area)
First, let's calculate the area of the glass window:
Area = Length * Width
= 5 ft * 8 ft
= 40 ft²
Now, substitute the values into the resistance formula:
Resistance = 0.025 ft / (5.5 BTU/ft²⋅hr⋅°F/inch * 40 ft²)
= 0.025 ft / (5.5 * 12/0.025)
= 0.025 ft / (5.5 * 12/0.025)
= 0.025 ft / (5.5 * 480)
= 0.025 ft / 2,640
= 0.0000095 ft²⋅hr⋅°F/BTU
Therefore, the resistance is approximately 0.0000095 ft²⋅hr⋅°F/BTU.
To find the driving force, we can use Ohm's Law for heat conduction:
Driving force = Temperature difference / Resistance
Substitute the known values into the formula:
Driving force = 1°F / 0.0000095 ft²⋅hr⋅°F/BTU
= 105,263.16 BTU/hr
Therefore, the driving force is approximately 105,263.16 BTU/hr.
To find the heat conducted in BTU per day, we can use the formula:
Heat conducted = Heat flux * Area * Time
First, let's convert time to hours:
1 day = 24 hours
Now, substitute the known values into the formula:
Heat conducted = 105,263.16 BTU/hr * 40 ft² * 24 hours
= 100,960,000 BTU
Therefore, the heat conducted in BTU per day is approximately 100,960,000 BTU.