How much thermal energy will flow per hour through a copper rod 5.00 cm in diameter and 1.50 m long, if one end of the rod is maintained at a temperature of 22.5 degree Celsius and the other end at 20.0 degree Celsius?
To calculate the thermal energy flow per hour through a copper rod, we need to use the equation for thermal conduction. The equation is:
Q = (k * A * ΔT) / L
where:
Q is the thermal energy flow (in Joules)
k is the thermal conductivity of copper (in Watts per meter-kelvin)
A is the cross-sectional area of the rod (in square meters)
ΔT is the temperature difference across the rod (in Kelvin)
L is the length of the rod (in meters)
First, let's convert the measurements to the appropriate units:
diameter = 5.00 cm, so the radius (r) = 5.00 cm / 2 = 2.50 cm = 0.025 m
length (L) = 1.50 m
temperature difference (ΔT) = 22.5°C - 20.0°C = 2.5°C = 2.5 K (since 1°C = 1 K)
Now we need to find the cross-sectional area (A) of the rod, which can be calculated using the formula for the area of a circle:
A = π * r^2
A = 3.14 * (0.025 m)^2
A = 0.0019635 m^2
We also need to find the thermal conductivity (k) of copper, which is approximately 386 Watts per meter-kelvin.
Now we have all the values we need to calculate the thermal energy flow (Q):
Q = (386 W/mK * 0.0019635 m^2 * 2.5 K) / 1.50 m
Q = 1.019 J/s
Finally, to find the thermal energy flow per hour, we need to convert the units:
Q_per_hour = (1.019 J/s) * (3600 s/h)
Q_per_hour = 3670.4 J/h
Therefore, the thermal energy flow per hour through the copper rod is approximately 3670.4 Joules.