How to I calculate the final temperature of aluminum in water with the mass and temperature of both substances?

Question

A 1.00kg piece of aluminum metal at 90.0°C is placed in 4.00 kg of water at 25.0°C. Determine the final temperature.

What equation do I use?

Answer 1

T = final temperature

T₁ = initial temperature of the hot aluminum

c₁ = specific heat of aluminum (look it up in appropriate units)

m₁ = mass the the aluminum piece

T₂ = initial temperature of the cold water

c₂ = specific heat of liquid water (look it up in appropriate units)

m₂ = mass of the water

Energy conservation requires that

m₁c₁(T₁ - T) = m₂c₂(T - T₂)

Plug in the numbers and solve for T.