A tap supplies water at 30°C while another supplies at 86°C. If a man wishes to bath with water at 44°C, calculate the ratio of mass of hot water to that of...

Answer Details

The ratio of hot water to cold water can be calculated using the principle of mixture of substances. Let m₁ be the mass of cold water required and m₂ be the mass of hot water required. The specific heat capacity of water is 4200 J/kg K. The heat gained by cold water, Q₁ = m₁ x 4200 J/kg K x (44 - 30) K The heat gained by hot water, Q₂ = m₂ x 4200 J/kg K x (86 - 44) K As per the principle of mixture of substances, the total heat gained by cold water is equal to the total heat lost by hot water. Hence, Q₁ = Q₂ Therefore, m₁ x 4200 J/kg K x (44 - 30) K = m₂ x 4200 J/kg K x (86 - 44) K Simplifying this equation gives us: m₂/m₁ = (44 - 30)/(86 - 44) = 14/42 = 1/3 Therefore, the ratio of mass of hot water to that of cold water required is 1:3. Hence, the answer is (a) 1:3.