The initial state of the system is comprised of (a) A metal sample m₁ = 43.5 g, mass T₁ = 100°C, temperature c₁ (unknown) specific heat, J/(g-C)
(b) Water m₂ = 39.9 g, mass T₂ = 25.1°C, temperature c₂ = 4.184 J/(g-C), specific heat
The final state of the system is M = m₁ + m₂, total mass T = 33.5°C, equilibrium temperature
Work in SI units. Note that changes in °C are equal to changes in °K. Equate change in total thermal energy to zero because the energy is conserved. m₁c₁(T-T₁) + m₂c₂(T-T₂) = 0 (43.5)*(c₁)(33.5 - 100) + (39.9)*(4.184)*(33.5 - 25.1) = 0 -2892.8c₁ + 1402.3 = 0 c₁ = 1402.3/2892.8 = 0.4848 J/(g-C)
Answer: The specific heat capacity of the metal is 0.485 J/(g-°C)
