A hot iron ball is dropped into a \(100 \text{ g}\) sample of water initially at \(30^\circ \)C. If 4.2 kJ of heat is transferred from the ball to the water, what is the final temperature of the water? (The specific heat of water is \(\pu{4.2 J/(g.^\circ \text{C})}\).)

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The heat transferred by the iron ball to the water.

$$ q_{\text{lost}}=q_{\text{gained}} $$ $$ \pu{4.2 kJ} = mc\Delta T $$ $$ \pu{4,200 } = 100(4.2)(T_f-30)$$ $$ 10 = T_f -30 $$ $$ T_f = \boxed{40} $$