# Heat Transfer Through a Copper Plate Let's determine the rate of heat transfer through the copper plate step by step. ## Given Data - **Area of the plate, \(A\):** 1 m² - **Thickness of the plate, \(d\):** .02 m - **Temperature on one side, \(T_1\):** 120°C - **Temperature on the other side, \(T_2\):** 80°C - **Thermal conductivity of copper, \(k\):** 400 W/m·K --- ## Step 1: Understand the heat conduction formula The rate of heat transfer (also called heat flux), \(Q\), through a material is given by Fourier's law: \[ Q = \frac{k \times A \times \Delta T}{d} \] Where: - \(Q\) = heat transfer rate in watts (W) - \(k\) = thermal conductivity - \(A\) = cross-sectional area - \(\Delta T\) = temperature difference across the material - \(d\) = thickness of the material --- ## Step 2: Calculate the temperature difference \[ \Delta T = T_1 - T_2 = 120^\circ C - 80^\circ C = 40^\circ C \] --- ## Step 3: Plug in the known values into Fourier’s law \[ Q = \frac{400 \times 1 \times 40}{.02} \] --- ## Step 4: Perform the calculation \[ Q = \frac{400 \times 40}{.02} = \frac{16,000}{.02} = 800,000\, \text{W} \] --- ## **Final Answer:** \[ \boxed{ \text{Rate of heat transfer } Q = \mathbf{800,000\, \text{W}} \quad \text{(or 800 kW)} } \] This is the rate at which heat is transferred through the copper plate from the hot side to the cold side.