Answer to Question #269773 in Molecular Physics | Thermodynamics for Fanah

Question

A 36.0g ice cube floats in 240g of water in a 100g copper cup,all are at a temperature of 0°C.A piece of lead at 99.0°C is dropped into the cup,and the final equilibrium temperature is 12.0°C.What is the mass of the lead?.(The heat of fusion and specific heat of water are 3.33×10^5 J/kg and 4,186 J/kg.°C, respectively.The specific heat of lead and copper are 128 J/kg.°C and 387 J/kg.°C).

Answer 1

By thermal equilibrium equation:

$$Q_i+Q_w+Q_c+Q_l=0,\\\space\\ m_i\lambda+c_wm_i(t_f-t_{ii})+c_wm_w(t_f-t_{iw})+\\+c_cm_c(t_f-t_{ic})+c_lm_l(t_f-t_{il})=0,\\\space\\ m_l=2363\text{ g}.$$