Question

(Schaum’s 18.25) A 55 g copper calorimeter (c=377 J/kg-K) contains 250 g of water (c=4190 J/kg-K) at 18o When a 75 g metal alloy at 100o C is dropped into the calorimeter, the final equilibrium temperature is 20.4o C. What is the specific heat of the alloy?

Answer 1

Answer:

1205.77 J/kg.K

Explanation:

Heat lost by alloy = heat gained by water + heat gained by the calorimeter

c₁m₁(t₂-t₃) = c₂m₂(t₃-t₁) + c₃m₃(t₃-t₁)................. Equation 1

Where c₁ = specific heat capacity of the alloy, m₁ = mass of the alloy, t₂ = initial temperature of the alloy, t₃ = equilibrium temperature, c₂ = specific heat capacity of water, m₂ = mass of water, t₁ = initial temperature of water and calorimter, c₃ = specific heat capacity of calorimter, m₃ = mass of calorimter.

Making c₁ the subject of the equation,

c₁ = c₂m₂(t₃-t₁) + c₃m₃(t₃-t₁)/m₁(t₂-t₃)........................ Equation 2

Given: c₂ = 4190 J/kgK, m₂ = 250 g = 0.25 kg, m₁ = 75 g = 0.075 kg, m₃ = 55 g = 0.055 kg, c₃ = 377 J/kg.K, t₁ = 18 °C, t₂ = 100 °C, t₃ = 24.4 °C.

Substitute into equation 2

c₁ = [0.25×4190×(24.4-18) + 0.055×377×(24.4-18)]/[0.075(100-24.4)]

c₁ = (6704+132.704)/5.67

c₁ = 6836.704/5.67

c₁ = 1205.77 J/kg.K

Thus the specific heat capacity of the alloy = 1205.77 J/kg.K