Question

A Styrofoam cup holds 0.297 kg of water at 23.5°C. Find the final equilibrium temperature (in degrees Celsius) after a 0.153 kg block of aluminum at 85.1°C is placed in the water. Neglect any thermal energy transfer with the Styrofoam cup. The specific heats of water and aluminum are cwater = 4186 J (kg · °C) and cAl = 900 J (kg · °C) .

°C

Answer 1

Mass of water = m₁ - 0.297 kg

Mass of the aluminium block = m₂ = 0.153 kg

Initial temperature of the water = T₁ = 23.5 ^oC

Initial temperature of the aluminium block = T₂ = 85.1 ^oC

Final equilibrium temperature = T₃

Specific heat of water = C₁ = 4186 J/(kg.^oC)

Specific heat of aluminium = C₂ = 900 J/(kg.^oC)

The heat lost by the aluminium block is equal to the heat gained by the water.

m₁C₁(T₃ - T₁) = m₂C₂(T₂ - T₃)

(0.297)(4186)(T₃ - 23.5) = (0.153)(900)(85.1 - T₃)

1243.242T₃ - 29216.187 = 11718.27 - 137.7T₃

1380.942T₃ = 40934.457

T₃ = 29.64 ^oC

Final equilibrium temperature = 29.64 ^oC