Neco 2024 Physics Question 13

A metal block of mass \(2.0\ \text{kg}\) and specific heat \(c_m = 0.45\ \text{kJ kg}^{-1}\text{K}^{-1}\) is initially at \(20\ ^\circ\text{C}\). It is placed in a well‑insulated water bath containing \(5.0\ \text{kg}\) of water (specific heat \(c_w = 4.18\ \text{kJ kg}^{-1}\text{K}^{-1}\)) at \(80\ ^\circ\text{C}\). The system loses heat to the surroundings at \(25\ ^\circ\text{C}\) according to Newton's law of cooling with a cooling constant \(k = 0.02\ \text{min}^{-1}\). (a) Assuming no heat loss, find the equilibrium temperature after mixing. (b) Using the equilibrium temperature as the initial temperature of the combined system, determine the temperature after \(10\) minutes of cooling. Give answers to one decimal place.