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)