Water at 50^ C is contained in a closed cylindrical vessel of height 10 cm and cross sectional area 10 cm ^2 . The walls of the vessel are adiabatic, while the flat parts are constructed of 1 -mm thick aluminium ( K = 200 J s ⁻¹ m ⁻¹ ^ C⁻¹ ). Assume the outside temperature is 20^ C . Given that the density of water is 1000 kg m ⁻³ and its specific heat capacity is 4200 J kg ⁻¹ ^ C⁻¹ , estimate the time taken for the

Step-by-step solution

Volume of water in the cylinder is given by: V = A h = 10 cm ^2 10 cm = 100 cm ^3 = 10⁻⁴ m ^3 Mass of the water is: m = V = 1000 kg m ⁻³ 10⁻⁴ m ^3 = 0.1 kg The heat lost by the water to cool by T = 1.0^ C is: Q = mc T = 0.1 4200 1.0 = 420 J Heat is lost only through the two flat parts (top and bottom) of the cylinder, as the walls are adiabatic. The total area for heat conduction is: A_ total = 2A = 2 10 cm ^2 = 2 10⁻³ m ^2 Assuming the temperature difference remains approximately constant at T_ cond = 50^ C - 20^