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
Want to see more full solutions like this?
Chapter 21 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- A rectangular window in a home has a length of 1.5 m and a height of 0.80 m. If the window allows heat to escape from the home at a rate of 2,000 watts, how thick must the window be if the inside temperature of the home is 220 C and the outside temperature is 3.00C? (Assume that the coefficient of thermal conduction of glass is 0.80 W/mK.) a. 7.1 mm b. 124 mm c. 9.1 mm d. 8.1 mm e. 11 mmarrow_forwardA certain amount of heat is added to a mass of aluminum (c=0.21 cal/g•°C), and its temperature is raised 57°C. Suppose that the same amount of heat is added to the same mass of copper (c=0.093 cal/g•°C). How much does the temperature of the copper rise? Answers: a. 3.2 x 10^2 degree Celsius b. 1.8 x 10^3 degree Celsius c. 1.3 x 10^2 degree Celsius d. 2.3 x 10^2 degree Celsiusarrow_forward01) A. An ice cube of mass 60 g is taken from a freezer at -15 °C and dropped into 100 g of water at 80°C. What will be the final temperature of the mixture? The specific heat capacity of ice is 2.04 kJ/kg °C · specific latent heat of fusion of ice is 334 kJ/kg, the specific heat capacity of water is 4.18 kJ/kg/°C B. A sphere of radius 0.500 m, temperature 27.0 C, and emissivity 0.850 is located in an environment of temperature 77.0 C. At what rate does the sphere (a) emit and (b) absorb thermal radiation? (c) What is the sphere’s net rate of energy exchange? (Stefan Boltzmann constant) = 5.67 x 10–8 W/m2 K4 C. A copper rod 24 cm long has cross-sectional area of 4 cm2. One end is maintained at 24°C and the other is at 184°C. What is the rate of heat flow in the rod? The heat Conductivity of copper is 397 W/m · °C. D. Below picture shows the composite wall block diagram. Calculate the thermal resistance of each blocks of A, B and C. Draw the thermal circuit diagram for the below…arrow_forward
- A copper cylinder has a mass of 0.0758 kg and a specific heat of 386 J/kg Co. It is heated to 80.5° C and then put in 0.0657 kg of unknown liquid whose temperature is 19.5° C. The final temperature of the mixture is 31.9° C. What is the specific heat of the unknown liquid? a. 875 J/kg C b. 1000 J/kg C c. 900 J/kg C d. 1745 J/kg Carrow_forwardA thermos contains m1=0.81kg of tea at T1=26 degrees Celcius. Ice (m2=0.065kg, T2=0 degrees celcius) is added to it. The heat capacity of both water and tea is c=4186J/(kg*K), and the latent heat of fusion for water is Lf=33.5x10^4 J/kg. a.) Find an expression for the final temperature after the ice has melted and the system has reached thermal equilibirum. b.) What is the final teperature in K.arrow_forwardThe heat flux in an aluminum pan containing boiling water is 5 × 10^5 W/m2. The temperature of the surface of the pan in contact with boiling water is 119 °C. a) Determine the temperature gradient in the pan on this surface. b) Determine an equation for calculating the temperature of the surface that is not in contact with water as a function of the thickness of the pan. c) What will be the temperature on the surface that is not in contact with water if the thickness of the pan is 1.2 mm? What if it's 4.0 mm? d) Evaluating the results obtained in questions "a", "b" and "c", how does the thickness of the pan influence the temperature gradient?arrow_forward
- A wood slab with a thickness of 0.05 m is subjected to a heat flux of 40 W/m2. The left and right surface temperatures of the wood slab are kept at constant temperatures of 40°C and 20°C, respectively. What is the thermal conductivity of the wood slab?arrow_forwardA 700 cm X 1360 cm house is built on a 13.2 cm thick concrete slab of thermal conductivity 0.62 W/m.K.. If the ground temperature of the slab is 7.9ºC while the interior of the house is 21.5ºC. Calculate the following: a) The temperature difference in kelvin. b) The temperature gradient (ΔT/Δx) in kelvin/metre. c) The heat loss rate through the concrete slab in kilowattarrow_forwardA 780 cm X 1320 cm house is built on a 12 cm thick concrete slab of thermal conductivity 0.68 W/m.K. If the ground temperature of the slab is 6.1°C while the interior of the house is 22.5°C.Calculate the following: a) The temperature difference in kelvin b) The temperature gradient (AT/Ax) in kelvin/metre c) The heat loss rate through the concrete slab in kilowattarrow_forward
- A 0.867 kg sample of ethanol is in its liquid state at its boiling temperature of 78 C. If 1.93e5 J of energy are transferred into the sample, what percentage of the sample is vaporized? ethanol has: a specific heat of 1000 J/kgK in solid form, a specific heat of 2010 J/kgK in liquid form, a freezing temperature of –114 C a boiling temperature of 78 C, a latent heat of fusion of 1.05e5 J/kg, and a latent heat of vaporization of 8.54e5 J/kgarrow_forwardThe tube in a heat exchanger has a 2-in inner diameter and a 3-in outer diameter. The thermal conductivity of the tube material is 0.5 Btu/h·ft·°F, while the inner surface heat transfer coefficient is 50 Btu/h·ft2·°F and the outer surface heat transfer coefficient is 10 Btu/h·ft2·°F. Determine the overall heat transfer coefficients based on the outer and inner surfaces.arrow_forwardOne end of an aluminum rod (50 cm long) is maintained at 1000C by immersing in a pot of boiling water and the other end at 00C by an ice-water mixture. If the cross-sectional area of the rod is 1.3 cm2, how much ice will the rod melt in 20 minutes? (thermal conductivity of Al is 205 W/m.0C) a) 0.19 kg b) 1.9 kg c) .019 kg Now consider the same situation, but the 50 cm long rod is half aluminum (25 cm) and half copper (25 cm). The aluminum end is in boiling water. The copper end is in the ice-water mixture. What would be the steady temperature of the Al-Cu junction? a) 50 0C b) 34.75 0C c) 65.25 0C How much ice will the rod melt in 20 minutes? a) 0.025 kg b) 0.25 kg c) 2.5 kgarrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON