A square steel bar of side length w = 0.13 m has a thermal conductivity of k = 14 J/(s?m??C) and is L = 2.8 m long.

1) The heat transferred to the cold end of the bar as a function of time can be calculated using the formula Q = kA(T1-T2)t/L, where Q is the heat transferred, k is the thermal conductivity, A is the cross-sectional area, T1 is the initial temperature of the hot end, T2 is the constant temperature of the cold end, t is the time elapsed, and L is the length of the bar. In this case, we can substitute w = 0.13 m for the side length of the square steel bar, giving A = w^2 = 0.0169 m^2. 2) To calculate the energy conducted in 1 hour, we can use the formula Q = kA(T1-T2)t/L and substitute T2 = 0°C and t = 1 hour = 3600 seconds. This gives Q = (14 J/(s·m·°C))(0.0169 m^2)(75°C-0°C)(3600 s)/(2.8 m) = 17311 J. 3) The mass of water melted in 1 hour can be calculated using the formula m = Q1/Lf, where Q1 is the heat transferred to the cold end of the bar in 1 hour and Lf is the latent heat of fusion. For water, Lf = 334 kJ/kg. Substituting the values, we get m = 17311 J / (334000 J/kg) = 0.0519 kg or 51.9 g of water melted in 1 hour.