Consider the water heater described in Problem 1.37. We now wish to determine the energy needed to compensate for heat losses incurred while the water is prescribed temperature of 55°C. The cylindrical storage tank (with flat ends) has a capacity of 100 gallons, and foamed urethane is used to insulate the side and end walls from ambient air at an annual average temperature of 20°C. The resistance to heat transfer is dominated by conduction in the insulation and by free convection in the air, for which h ≈ 2 W/m² ∙ K. If electric resistance heating is used to compensate for the losses and the cost of electric power is $0.08/kW ∙ h, specify tank and insulation dimensions for which the annual cost associated with the heat losses is less than $50.