Igcse Model Questions Vol1 2021 Physics Question 24

A \(250\ \text{g}\) block of copper at \(150^{\circ}\text{C}\) is placed into a calorimeter that initially contains \(500\ \text{g}\) of water at \(20^{\circ}\text{C}\). The calorimeter itself has a heat capacity of \(100\ \text{J °C}^{-1}\). No heat is lost to the surroundings. The specific heat capacities are: copper \(c_{\text{Cu}} = 385\ \text{J kg}^{-1}\text{°C}^{-1}\), water \(c_{\text{w}} = 4186\ \text{J kg}^{-1}\text{°C}^{-1}\). After the system reaches equilibrium the final temperature is \(30^{\circ}\text{C}\). Assuming that a certain mass of ice at \(0^{\circ}\text{C}\) was present in the water initially and melted during the experiment, determine the mass of ice (in grams) that must have been present.