Concept explainers
From Table 21.1, the specific heat of milk is 3.93 × 103 J/ (kg ∙ K). and the specific heat of water is 4.19 × 103 J/(kg ∙ K). Suppose you wish to make a large mug (0.500 L) of hot chocolate. Each liquid is initially at 5.00°C. and you need to raise their temperature to 80.0°C. The density of milk is about 1.03 × 103 kg/m3, and the density of water is 1.00 × 103 kg/m3. a. How much heat must be transferred in each case? b. If you use a small electric hot plate that puts out 455 W, how long would it take to heat each liquid?
(a)
The amount of heat transferred to milk and water.
Answer to Problem 20PQ
The amount of heat transferred to milk is
Explanation of Solution
Write the expression for heat energy transferred to the system.
Here,
Write the expression for mass of the milk, relating density and volume.
Here,
Write the expression for mass of the water, relating density and volume.
Here,
Rearrange the equation (I) to calculate the heat required for milk.
Here,
Rearrange the equation (I) to calculate the heat required for water.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the amount of heat transferred to milk is
(b)
The time taken to heat milk and water.
Answer to Problem 20PQ
The time taken to heat milk is
Explanation of Solution
Write the expression for power (energy per unit time).
Here,
Rearrange the above equation for
Rearrange the equation for time taken to heat the milk.
Here,
Rearrange the equation for time taken to heat the water.
Here,
Conclusion:
Substitute
Substitute
Therefore, the time taken to heat milk is
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Chapter 21 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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