During a winter day, the atmospheric temperature falls to -10^ C , and ice begins to form on the surface of a lake. Determine the rate of increase of the ice thickness when 10 cm of ice has already formed. Assume the temperature of the entire body of water reaches 0^ C prior to the onset of ice formation. Take the density of water as 1000 kg m ⁻³ , the latent heat of fusion of ice as 3.36 10^5 J kg ⁻¹ , and the therm

Step-by-step solution

The rate of heat conduction through the ice layer is given by: dQ dt = KA(T_w - T_a) x The rate of heat released due to the formation of ice of thickness dx is: dQ dt = A L dx dt Equating the two rates of heat transfer: A L dx dt = KA(T_w - T_a) x dx dt = K(T_w - T_a) L x Substituting the given values, K = 1.7 W m ⁻¹ ^ C ⁻¹ , T_w = 0^ C , T_a = -10^ C , = 1000 kg m ⁻³ , L = 3.36 10^5 J kg ⁻¹ , and x = 0.1 m : dx dt = 1.7 (0 - (-10)) 1000 3.36 10^5 0.1 dx dt = 17 3.36 10^7 dx dt 5.06 10⁻⁷ m s ⁻¹