Heat Gained = Heat Lost
q = ­q
Sample Problems
1. 50.0 g of water at 15.0°C is mixed with 75.0 g of water at 80.0°C. What is the final temperature of the water?
2. Calculate the final water temperature if 100.0 g of ice at –50.0°C is mixed with 400.0 g of water at 80.0°C.
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1. 50.0 g of water at 15.0°C is mixed with 75.0 g of water at 80.0°C. What is the final temperature of the water?
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2. Calculate the final water temperature if 100.0 g of ice at –50.0°C is mixed with 400.0 g of water at 80.0°C.
Heat gained = Heat lost
q = ‐q
ice water
‐50°C g T f 80.0°C
(‐50.0°C g 0.0°C) + (melt) + (0.0°C g Tf) = – [(80.0°C g Tf)]
(mcΔT﴿ + (nΔHfus) + (mcΔT﴿ = – [﴾mcΔT﴿]
(0.1000 kg)(2.06 kJ/kg°C)(50.0°C) + (5.551 mol)(6.03 kJ/mol) + (0.1000 kg)(4.18 J/kg°C)(Tf – 0.0°C) = – [(0.4000 kg)( 4.18 kJ/kg°C)(Tf – 80.0°C)
10.3 kJ + 33.472 kJ + 0.418 kJ/°C Tf – 0 kJ = – [1.672 kJ/°C Tf – 133.76 kJ]
10.3 kJ + 33.472 kJ + 0.418 kJ/°C Tf – 0 kJ = ‐1.672 kJ/°C Tf + 133.76 kJ
0.418 kJ/°C Tf + 1.672 kJ/°C Tf = 133.76 kJ – 10.3 kJ – 33.472 kJ
2.09 kJ/°C Tf = 89.988 kJ
Tf = 43.1°C
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