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.
Qcold=m1m2c(T1−T2)m1+m2Q_{cold}=\frac{m_1m_2c(T_1-T_2)}{m_1+m_2}
problems.proof.analysis

Check against a limiting case, a stated condition, or an energy balance. A sound result must have the expected physical trend.