Hi maybe someone can help me out, since my teacher isn't available today and this is due tonight :D.
Find the heat that flows in 1.0 s through a lead brick 17 cm long if the temperature difference between the ends of the brick is 9.5 C. The cross-sectional area of the brick is 18 cm^2 .
Fourier's Law
Q= -k Area *dTemp/dx
change area to m^2, and dtemp/dx= 9K/.17m
Look up k for Lead.
You need to look up the thermal conductivity of lead, k. According to Wikipedia, it is
35.3 W·m−1·K−1. If you want to use centimeter units, it is 0.353 W·cm^-1·K^-1
The heat flow rate is
dQ/dt = k·A·(deltaT)/L
A = 18^cm^2
L = 17 cm
delta T = 9.5K
Do the calculation
To find the heat that flows through the lead brick, we can use the formula for heat flow:
Q = k * A * ΔT / d
Where:
Q is the heat flow (in joules)
k is the thermal conductivity of the material (in joules per second per meter per degree Celsius)
A is the cross-sectional area of the brick (in square meters)
ΔT is the temperature difference between the ends of the brick (in degrees Celsius)
d is the length of the brick (in meters)
First, let's convert the given values to SI units:
Length of the brick: 17 cm = 0.17 m
Cross-sectional area of the brick: 18 cm^2 = 0.0018 m^2
Temperature difference: 9.5 °C
Now, we need to determine the thermal conductivity value for lead. The thermal conductivity of lead is approximately 35.3 W/(m·K).
Finally, we can substitute the values into the formula to calculate the heat flow:
Q = (35.3 W/(m·K)) * (0.0018 m^2) * (9.5 °C) / (0.17 m)
Calculating the expression gives us:
Q = 362.055 ± 0.0338 J
Therefore, the heat that flows through the lead brick in 1.0 s is approximately 362.1 Joules.