Question

# A Styrofoam cup holds 0.297 kg of water at 23.5°C. Find the final equilibrium temperature (in...

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

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