An iron calorimeter weighing 10 g contains water weighing 500 g at a temperature of 15 degrees Celsius, when an aluminum

An iron calorimeter weighing 10 g contains water weighing 500 g at a temperature of 15 degrees Celsius, when an aluminum bar with a temperature of 100 degrees Celsius was immersed in water, the water temperature increased by 2 degrees, determine the mass of the bar. Determine the mass of the bar.

A hot aluminum bar will heat the water and the calorimeter itself until all temperatures are equal and thermal equilibrium occurs. According to the condition of the problem, this occurs at a temperature of 15 + 2 = 17 ° C.

Let be
m is the mass of an aluminum bar
m₁ – mass of water 0.5 kg
m₂ – calorimeter mass 0.1 kg
c – specific heat of aluminum 920 J / (kg * ° С)
c₁ – specific heat capacity of water 4220 J / (kg * ° С)
c₂ – specific heat of iron 460 J / (kg * ° С)
ΔT – decrease in bar temperature 100 – 17 = 87 ° С
Δt – increase in water and calorimeter temperatures 17 – 15 = 2 ° С
Q – heat given off by aluminum
Q₁ – heat received by water
Q₂ – heat received by the calorimeter

Let’s compose the heat balance equation and express m:
Q = Q₁ + Q₂
cmΔT = c₁m₁Δt + c₂m₂Δt
m = Δt (c₁m₁ + c₂m₂) ÷ (cΔT)
m = 2 ∙ (4220 ∙ 0.5 + 460 ∙ 0.1) ÷ 920 ∙ 87
m = 0.054

Answer: the mass of the bar is 54 grams.