A metal sample weighing 43.5 g and at a temperature of 100.0 °c was placed in 39.9 g of water in a calorimeter at 25.1 °c. at equilibrium, the temperature of the water and metal was 33.5 °c. determine the specific heat capacity of the metal.

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)