A student conducts an experiment to determine the specific heat capacity \(c_s\) of an unknown solid sample of mass \(m_s\). The sample is heated to an initial temperature \(T_s\) and placed into a calorimeter container of mass \(m_c\) and specific heat capacity \(c_c\). The container holds a mass \(m_w\) of water with specific heat capacity \(c_w\), initially at temperature \(T_i\) (where \(T_s > T_i\)). The system reaches a final equilibrium temperature \(T_f\) after a time interval \(\Delta t\), during which heat is lost to the surroundings at a constant rate \(P_{\text{loss}}\). Which of the following is a correct expression for \(c_s\)?