Question

Hot water added to cold water spontaneously mixes so that all of the water has the same average temperature. State and apply the laws of thermodynamics to explain this process.

Answer 1

LAW OF CONSERVATION OF ENERGY

Adding equal amounts of hot water and cool water produces a final temperature halfway between the initial temperatures of both. When the proportions of the hot and cold water were varied, the temperature changed. The final temperature was somewhere between the two initial temperatures, and nearer to the temperature of the water with the larger mass. The law of conservation of energy informs us that if the cold water gained thermal energy through the transfer of heat, then the hot water must have lost an equal amount of thermal energy. The total energy change must be zero. An equation to express this might look as follows:

Δ Q_h + ΔQ_c =0

m_h (T_f -T_h) + m_c (T_f -T_c) =0