A chunk of aluminum weighing 19.7 grams and originally at 98.01 °C is dropped into an insulated cup containing 81.3 grams of water at 21.05 °C. Assuming that all of the heat is transferred to the water, the final temperature of the water is

T (final) = 35°C

Explanation:

Use ∑ (heat flows) = ∑q = 0

q (Al) + q (H₂O) = (mcΔT) Al + (mcΔT) H₂O = 0

[ (19.7g) (0.91cal/g°C) (T (f) - 98.01°C) ] + [ (81.3g) (1.00cal/g°C) (T (f) - 21.05°C) ] = 0

Collecting terms and solving for T (f) = 35°C final mix temperature