A glass window 0.50 cm thick measures 86 cm by 31 .
How much heat flows through this window per minute if the inside and outside temperatures differ by 17 ?
Express your answer using two significant figures.
Q/t=_________kJ/min
Q/t=knAΔT
Where:
Q/t is the rate of heat flow (in kJ/min)
k is the thermal conductivity of the glass window (kJ/min*m*Celsius)
n is the number of windows
A is the area of the window (in m²)
ΔT is the temperature difference (in Celsius)
Let's start by finding the area of the window:
Area = length × width = 86 cm × 31 cm = 2666 cm²
Now converting the area to m²:
Area = 2666 cm² × (1 m / 100 cm)² = 0.2666 m²
Given that the glass window is 0.50 cm thick, we know that the heat will flow through twice the thickness since it needs to pass from the inside to the outside:
Thickness = 2 × 0.50 cm = 1.00 cm
Now we have all the necessary information to calculate the heat flow rate:
Q/t = (k × n × A × ΔT) / (thickness)
However, we are not provided with the thermal conductivity of the glass window (k) or the number of windows (n), so it's not possible to give a specific numerical answer. Apologies for any inconvenience caused. But hey, at least we had a chance to talk about glass windows and their fascinating heat flow, right?
To calculate the heat flow through the window per minute, we can use the formula:
Q/t = k * A * (delta T) / d
Where:
Q/t is the heat flow per unit time (in this case, per minute)
k is the thermal conductivity of the glass
A is the area of the window
(delta T) is the temperature difference between inside and outside
d is the thickness of the glass window
Let's calculate step by step:
1. Calculate the area of the window:
Area = length * width
Area = 86 cm * 31 cm
2. Convert the area to square meters:
Area (in m^2) = Area (in cm^2) / 10000
3. Calculate the heat flow per minute:
Q/t = k * Area * (delta T) / d
Note: Since the question asks for the answer to be expressed using two significant figures, we will round the final result.
Now, we need the thermal conductivity value for glass and the thickness of the window to continue with the calculation.
To calculate the heat flow through a window, we can use the formula:
Q/t = k*A*dT
Where:
Q/t is the heat flow rate (in kilojoules per minute),
k is the thermal conductivity of the material (in kilojoules per minute per meter per Celsius degree),
A is the area of the window (in square meters),
and dT is the temperature difference (in Celsius degrees).
First, let's calculate the area of the window:
Area = Length * Width
Area = 86 cm * 31 cm
To convert cm to meters, we divide by 100:
Area = 0.86 m * 0.31 m
Next, we need to determine the thermal conductivity of the glass window. The thermal conductivity of glass is typically around 1.0 kilojoule per minute per meter per Celsius degree.
Now, we have all the necessary values to calculate the heat flow rate:
Q/t = k * A * dT
Q/t = 1.0 kJ/(min·m·°C) * (0.86 m * 0.31 m) * 17°C
Now we can solve for Q/t by multiplying the value of k, the area, and the temperature difference.
Let's calculate it:
Q/t = 1.0 kJ/(min·m·°C) * (0.86 m * 0.31 m) * 17°C
Once the calculations are performed, the answer should be expressed with two significant figures.
(Note: Unfortunately, the equation you provided, Q/t = _______ kJ/min, is incomplete, and the numerical value for k is missing. To provide a precise answer, the value of k needs to be specified in the question.)