Find the heat that flows in 1 s through a lead brick 18 cm long if the temperature difference between the ends of the brick is 6.8° C. The cross-sectional area of the brick is 14 cm2.
To find the heat that flows through the lead brick, we can use the formula for heat transfer known as Fourier's Law of Heat Conduction:
Q = k * A * (ΔT / L)
Where:
Q = Heat transfer (in calories or joules)
k = Thermal conductivity of the material (in calories per second per cm per degree Celsius or joules per second per meter per Kelvin)
A = Cross-sectional area of the material (in cm^2 or m^2)
ΔT = Temperature difference (in degrees Celsius or Kelvin)
L = Length of the material (in cm or m)
Given:
ΔT = 6.8°C
L = 18 cm
A = 14 cm^2
We need to convert the units to be consistent, so we can either convert all the units to centimeters or convert them all to meters. Let's convert them to meters for this calculation:
ΔT = 6.8°C = 6.8 K (since 1°C = 1 K)
L = 18 cm = 0.18 m
A = 14 cm^2 = 0.0014 m^2
Now we can substitute the values into the formula:
Q = k * A * (ΔT / L)
We need to know the thermal conductivity of lead in order to complete the calculation, as it is missing from the given information. Can you provide the value of the thermal conductivity of lead?
To find the heat that flows in 1 second through the lead brick, we can use the formula:
Q = k * A * ΔT / L
where:
Q is the heat flow
k is the thermal conductivity of the material (in this case, lead)
A is the cross-sectional area of the brick
ΔT is the temperature difference between the ends of the brick
L is the length of the brick
To answer this question, we need to know the thermal conductivity of lead. The thermal conductivity of lead is approximately 35 W/(m*K). However, in this case, the units for length, area, and temperature difference are given in centimeters and degrees Celsius. We need to convert these to meters and Kelvin, respectively, before performing the calculation.
1. Convert the length from centimeters to meters:
L = 18 cm ÷ 100 cm/m = 0.18 m
2. Convert the cross-sectional area from square centimeters to square meters:
A = 14 cm^2 ÷ (100 cm/m)^2 = 0.0014 m^2
3. Convert the temperature difference from degrees Celsius to Kelvin:
ΔT = 6.8 °C + 273.15 °C = 280.95 K
Now we have all the values required to calculate the heat flow:
Q = (35 W/(m*K)) * (0.0014 m^2) * (280.95 K) / (0.18 m)
= 11.27 W
Therefore, the heat that flows in 1 second through the lead brick is approximately 11.27 Watts (W).
Look up the thermal conductivity of lead, k, and use the heat conduction equation.
Q = k*A*(dT/dX)*1 second
A = 14 cm^2
dT/dX is the temperature gradient, 0.378 degC/cm
k should be in units of calories or joules per (degC*cm)