Neco 2025 Physics Question 5

A \(150\,\text{g}\) copper block (specific heat \(c_{\text{Cu}} = 0.385\,\text{J\,g}^{-1}\,\text{K}^{-1}\)) initially at \(80^{\circ}\text{C}\) is placed into \(200\,\text{g}\) of water (specific heat \(c_{\text{w}} = 4.18\,\text{J\,g}^{-1}\,\text{K}^{-1}\)) initially at \(20^{\circ}\text{C}\) inside an insulated container. The system reaches equilibrium at \(70^{\circ}\text{C}\) after \(300\) s. During this time the container loses heat to the surroundings (ambient temperature \(15^{\circ}\text{C}\)) at a rate \(\dot Q = k\,(T_{\text{avg}}-T_{\text{amb}})\) with \(k = 0.02\,\text{J\,s}^{-1}\,\text{K}^{-1}\).\n(a) What would the final temperature be if there were no heat loss?\n(b) How much total heat was lost to the surroundings during the 300 s?