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Answer :
A 65.0 g sample of copper at 97.6 °C is added to 46.1 g of water at 20 °C, reaching a final temperature of 24.9 °C.
What does the law of conservation of energy state?
In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time.
- Step 1: Calculate the heat lost by the sample of copper.
A 65.0 g (m) sample of copper is cooled from 97.6 °C to 24.9 °C. Given that its specific heat (c) is 0.20 J/g.°C, we can calculate the heat (Q) lost using the following expression.
Q(Cu) = c(Cu) × m(Cu) × ΔT
Q(Cu) = (0.20 J/g.°C) × 65.0 °C × (24.9 °C - 97.6 °C) = -945 J
- Step 2: Calculate the heat gained by the water (Qw).
We will use the law of conservation of energy.
Qw + Q(Cu) = 0
Qw = -Q(Cu) = 945 J
- Step 3: Calculate the mass of water.
We will use the same expression as in Step 1.
Qw = c(w) × m(w) × ΔT
m(w) = Qw / c(w) × ΔT
m(w) = 945 J / (4.18 J&g.°C) × (24.9 °C - 20 °C) = 46.1 g
A 65.0 g sample of copper at 97.6 °C is added to 46.1 g of water at 20 °C, reaching a final temperature of 24.9 °C.
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