Physic Labs

Problem 2

Two masses of water m1,m2m_1,m_2 initially at temperatures T1>T2T_1>T_2 are mixed in an insulated vessel. Neglect vessel heat capacity, heat loss, and evaporation; water’s specific heat cc is constant and no phase change occurs. (a) Write the heat balance and find final temperature TfT_f. (b) Find heat gained by the colder water. (c) For m1=2m2m_1=2m_2, locate TfT_f between the initial temperatures. Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.
Q1=m1c(Tf−T1)Q_1=m_1c(T_f-T_1)
problems.proof.analysis

Apply the governing law for the stated model, using the sign convention in the problem. This provides the starting equation for the later parts.

problems.proof.pitfall. Insulation does not keep each water sample at its initial temperature; heat lost equals heat gained.