Halliday, Resnick & Walker — Temperature, Heat, and the First Law of Thermodynamics: Problem 37

A person makes a quantity of iced tea by mixing 500 g of hot tea (essentially water) with an equal mass of ice at its melting point. Assume the mixture has negligible energy exchanges with its environment. If the tea’s initial temperature is \( T_i = 90^\circ\text{C} \), when thermal equilibrium is reached what are (a) the mixture’s temperature \( T_f \) and (b) the remaining mass \( m_f \) of ice? If \( T_i = 70^\circ\text{C} \), when thermal equilibrium is reached what are (c) \( T_f \) and (d) \( m_f \)?