Question

A 54g copper calorimeter contains 80cm3 at 20∘C. A very cold 110g copper cylindrical sample is dropped into the water causing the water to partially freeze, with 5cm3 being converted to ice. The final temperature of the system is 0∘C. What is the initial temperature in Kelvins of the cylindrical sample?

Answer 1

$$m_cc_c(T_0-T)+m_wc_w(T_0-T)+m_iL\\=Mc_c(T-T')\\ (0.054)(385)(20-0)+(4200)(80\cdot10^{-6})(1000)(20-0)\\+(5\cdot10^{-6})(1000)(334000)=(0.11)(385)(0-T')$$

$$T'=-208\degree C=273-208=65\ K$$