The left end of a copper rod (length = 20 cm , area of cross section = 0.20 cm ^2 ) is kept at 20^ C while the right end is kept at 80^ C . Ignoring any heat loss due to radiation, determine the heat current through the rod. Thermal conductivity of copper = 385 W m ⁻¹ ^ C ⁻¹ .

Step-by-step solution

Given parameters of the copper rod: Length, L = 20 cm = 0.20 m Area of cross section, A = 0.20 cm ^2 = 0.20 10⁻⁴ m ^2 Temperature difference, T = 80^ C - 20^ C = 60^ C Thermal conductivity, k = 385 W m ⁻¹ ^ C ⁻¹ The heat current H through the rod is given by Fourier's law of heat conduction: H = k A T L Substituting the given values: H = 385 0.20 10⁻⁴ 60 0.20 H = 385 10⁻⁴ 60 H = 23100 10⁻⁴ H = 2.31 J s ⁻¹