Hot water that is 78.0°C is to be mixed with 4L of cold water that is 23.0°C. What should be the amount of hot water for them to have a final temperature of 24°C?

Chemistry: Matter and Change
1st Edition
ISBN:9780078746376
Author:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl Wistrom
Publisher:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl Wistrom
Chapter15: Energy And Chemical Change
Section: Chapter Questions
Problem 126A
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Hot water that is 78.0°C is to be mixed with 4L of cold water that is 23.0°C. What should be the amount of hot water for them to have a final temperature of 24°C?

Expert Solution
Step 1

When water at two different temperatures is mixed, the temperature of cold tap water increases and hot tap water decreases till the whole mixture gets same temperature.

Energy lost by the hot water which is at 78.0oC (exothermic) and energy gained by the cold water that is at 23.0oC is equal at thermal equilibrium (24.0oC).

Change in temperature is,

ΔT=Tf-TiΔTcold water=24°C-23°C=1°CΔThot water=24°C-78.0°C=-54°C

Density of water is 1000.0 g/mL. Thus, mass of cold water is,

Mass=Density×Volume          =1000 g/L4 L=4000 g

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