Heat Transfer and Thermal Equilibrium Practice Test

A 40.0 g piece of aluminum at $90^\circ\text{C}$ is placed into 200.0 g of water at $25^\circ\text{C}$ in an insulated calorimeter. Use $c_{\text{Al}}=0.90\ \text{J g}^{-1}!!\cdot!^\circ\text{C}^{-1}$ and $c_{\text{water}}=4.18\ \text{J g}^{-1}!!\cdot!^\circ\text{C}^{-1}$. Assume heat lost equals heat gained. Which of the following is the correct energy-balance equation to solve for the final temperature $T_f$?

A 50.0 g piece of metal at $80^\circ\text{C}$ is placed into 100.0 g of water at $20^\circ\text{C}$ in an insulated cup. The specific heat capacities are $c_{\text{metal}}=0.50\ \text{J g}^{-1}!!\cdot!^\circ\text{C}^{-1}$ and $c_{\text{water}}=4.18\ \text{J g}^{-1}!!\cdot!^\circ\text{C}^{-1}$. Assume no heat is lost to the surroundings, so heat lost by the metal equals heat gained by the water. Which statement best describes the direction of heat flow and the final equilibrium temperature?