What will be the equilibrium temperature when a 235 gg block of copper at 255 ∘C∘C is placed in a 155 gg aluminum calorimeter cup containing 875 gg of water at 16.0 ∘C∘C?

The answer to the question is

The equilibrium temperature T = 22.016 °C

Explanation:

To solve the question, we note the given variables thus

Mass of copper block =235 grams

Temperature of the copper block = 255 °C

Mass of aluminium calorimeter cup = 155 g

Mass of water in calorimeter cup = 16 °C

Also we note the specific heat capacities of the materials involved in the question

Specific heat capacity of water = 4.186 joule/gram

Specific heat capacity of copper= 0.385 joule/gram

Specific heat capacity of aluminium = 0.900  joule/gram

There for from the first law of thermodynamics, energy is neither created nor destroyed but it changes from one form to another, we have

Heat lost by copper = heat gained by water and the calorimeter cup

Therefore we have

The equation for heat capacity =

mass * specific heat capacity * Temperature change  = m·c·ΔT

therefore

m·c·ΔT for copper = m·c·ΔT for aluminium + m·c·ΔT for water

where ΔT on the left of the equation = Initial temperature - final temperature

while on the right  ΔT = Final temperature - Initial temperature

and the final temperature in this case = the equilibrium temperature

255*0.385*(255 -T) = 155*0.9*(T-16) +875*4.186*(T-16)

Which gives the equilibrium temperature T = 22.016 °C