Show that the thickness of the ice on a lake increases with the square root of the time in cold weather, making the following simplifying assumptions. Let the water temperature be a constant 10◦C, the air temperature a constant −10◦, and assumethat at any given time the ice forms a slab of uniform thickness x. The rate of formation of ice is proportional to the rate at which heat is transferred from the water to the air. Let t = 0 when x = 0

Show that the thickness of the ice on a lake increases with the square root of the time in cold weather, making the following simplifying assumptions. Let the water temperature be a constant 10◦C, the air temperature a constant −10◦, and assumethat at any given time the ice forms a slab of uniform thickness x. The rate of formation of ice is proportional to the rate at which heat is transferred from the water to the air. Let t = 0 when x = 0

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter1: Temperature And Heat

Section: Chapter Questions

Problem 119AP: For the human body, what is the rate of heat transfer by conduction through the body's tissue with...

See similar textbooks

Related questions

Q: Obtain a relation for the time required for a lumped systemto reach the average temperature 1/2(Ti +…

A: Given,

Q: In exercising, a weight lifter loses 0.197 kg of water through evaporation, the heat required to…

Q: A heavy hydrocarbon oil which has a Cp = 2.30 kJ/kg.K is being cooled in a heat exchanger from 371.9…

Q: A sheet of metal lies on a roof which is inclined at an angle 0. The coefficient of kinetic friction…

A: The change in length due to thermal expansion is, ∆L=αL∆T

Q: A body with mass of 1 kg slides downwards on an inclined plane of height equals 2 m. The angle of…

Q: Consider the lengths of three metal rods at different temperatures as shown below. Which of the…

Q: Suppose you want to raise the temperature of a mass m of ice from T0 100 °C. In this problem,…

Q: Suppose that the liquid film in Fig. 7-4 has temperature variations that are large enough to alter…

Q: The value of the specific heat of a gas whose molecules are tetrahedral and is restricted by six…

A: The molecules of the gas shows tetrahedral structure. So number of atoms N=5 There are 6…

Q: Assume that 50 % of the potential energy of a rain- drop turns into internal energy of the drop, as…

A: Relation between potential energy and internal energy of drop according to the question, 12PE=U…

Q: Explain how the maximum possible heat transferrate Q.max in a heat exchanger can be determined when…

Q: A perfectly insulating cylindrical glass is partially full of water. At the top of the water is a…

A: Write the expression for the rate of heat flow when the thickness of the layer is y, and write an…

Q: A system gains 3080 J of heat at a constant pressure of 1.28 × 105 Pa, and its internal energy…

Q: The rectangular plate has a length of l and width of w. If the temperature increases by ΔT, find the…

Q: A system gains 3310 J of heat at a constant pressure of 1.38 × 105 Pa, and its internal energy…

A: Write the given values with suitable variables.

Q: Consider a surface of area A at which the convection and radiation heat transfer coefficients are…

A: We are given a surface of area A, at which the convection and radiation heat transfer coefficients…

Q: 2.60 A plane wall with constant properties is initially at a uni- form temperature T, Suddenly, the…

Q: A test is conducted to determine the overall heat transfer coefficient in anautomotive radiator that…

A: Given data: The number of tubes in the radiator is n = 40 tubes. The internal diameter of the…

Q: Consider a block of ice, with a mass of 2.00 kg and an initial temperature of -8.00°C. Given the…

Q: 4. Newton showed that the rate of change of temperature is proportional to the temperature…

Q: Star A has twice the radius and triple absolute temperature of star B. What is the rati of the power…

Q: Saturated steam at 1 atm condenses on a vertical plate that is maintained at 90°C by circulating…

A: Using table A-5, the enthalpy of vaporization of water at 1 atm,

Q: A 49.0 g sample of quartz, which has a specific heat capacity of 0.730 J-g .°C *, Is dropped into an…

A: Given quantities: mass of quartz sample (m) = 49 g specific heat capacity of quartz (C) = 0.730…

Q: The ceiling of a single-family dwelling in a cold climate should have an R-value of 30. To give such…

A: Insulation thickness The given R-value is taken in I-P units which are then converted into SI units…

Q: Consider a 3-m-high rectangular enclosure consisting of two surfaces separated by a 0.1-m air gap at…

Q: The basic principle of calorimetry states that: In an isolated system whose parts interact by heat…

A: This question is based on Thermodynamics topic. The principle of calorimetry is based on…

Q: 1.900 x 10° J of heat is added to a cylinder of aluminum (radius 5.000 cm, length 10.00 cm) at room…

A: Given Length= 10 cm Initial Temperature= 300K

Q: Estimate the rate at which heat can be conducted from theinterior of the body to the surface. As a…

A: The rate at which the heat can be conducted from the interior of a body to the surface is given by;…

Q: A furnace is shaped like a long equilateral-triangularduct where the width of each side is 2 m. Heat…

Q: A 50-m-long section of a steam pipe whose outer diameteris 10 cm passes through an open space at…

Q: A Dallas home has their thermostat set at 70 °F. During a hot summer day, the power suddenly cut off…

A: Given, The temperature of the surrounding Ts= 80°F dTdt=2°F/hr k=0.5 per hour

Q: Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 m2, are placed end to end as…

A: Given Two bars A and B kept side by side.

Q: Suppose that the initial temperature difference between an object and its surroundings is D0 and the…

A: Given :- initial temperature difference between an object and its surrounding = D0…

Q: The specific heat of a substance varies with temperature according to the function c = 0.20 + 0.14T…

Q: Suppose same amounts of heat transfer (Q) into different masses of copper and water, causing same…

A: Heat transfer to copper and water are the same

Q: A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R.…

Q: Show that the coefficient of area expansion, (∆A/A)/∆T, of a rectangular sheet of the solid is twice…

A: The expression for the coefficient of linear expansion is

Q: Consider an ordinary shower where hot water at 140°F is mixed with cold water at 50°F. If it is…

Question

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

If you place 0 ice into 0 water in an insulated container, what will the net result be? Will there be less ice and more liquid water, or more ice and less liquid water, or will the amounts stay the same?
Consider the latent heat of fusion and the latent heat of vaporization for H2O, 3.33 105 J/kg and 2.256 106 J/kg, respectively. How much heat is needed to a. melt 2.00 kg of ice and b. vaporize 2.00 kg of water? Assume the temperatures of the ice and steam are at the melting point and vaporization point, respectively. (a). UsingEq21.9, Q = mLF = (2.00 kg) (3.33l05 J/kg) = 6.66105 J (b).UsingEq21.10. Q = mLV = (2.00kg) (2.256106 J/kg) = 14.51106 J
For the human body, what is the rate of heat transfer by conduction through the body's tissue with the following conditions: the tissue thickness is 3.00 cm, the difference in temperature is 2.00 , and the skin area is 1.50 m2. How does this compare with the average heat transfer rate to the body resulting from an energy intake of about 2400 kcal per day? (No exercise is included.)
For a temperature increase of 10 at constant volume, what is the heat absorbed by (a) 3.0 mol of a dilute monatomic gas; (b) 0.50 mol of a dilute diatomic gas; and (c) 15 mol of a dilute polyatomic gas?
The height of the Washington Monument is measured to be 170.00 m on a day when the temperature is 35.0 . What will its height be on a day when the temperature falls to -10.0 ? Although the monument is made of limestone, assume that its coefficient of thermal expansion is the same as that of marble. Give your answer to five significant figures.
A body with mass of 1 kg slides downwards on an inclined plane of height equals 2 m. The angle of inclination is 30°, and the friction coefficient 0.2. Find the amount of heat released as a result of the friction. /Give the answer in [J] /
Suppose you want to raise the temperature of a mass m of ice from T0 < 0 °C to T > 100 °C. In this problem, represent the heat of fusion as Lf, the heat of vaporization as Lv, and the temperatures at which the phase changes occur as Tf and Tv. How much heat must be transferred for this to happen, including the energy needed for phase changes? Your answer should be in terms of the variables in the introduction and the specific heats of ice (ci), water (cw), and steam (cs). The talent heats are Lf= 334kJ/kg and Lv=2256kJ/kg?
The rectangular plate has a length of l and width of w. If the temperature increases by ΔT, find the increase of the area of the plate, given that the coefficient of the linear expansion of the plate material is α.
Saturated steam at 1 atm condenses on a vertical plate that is maintained at 90°C by circulating cooling water through the other side. If the rate of heat transfer by condensation to the plate is 180 kJ/s, determine the rate at which the condensate drips off the plate at the bottom.
The 10 m long pipe has an inner radius of 70 mm, an outer radius of 80 mm, and is made of stainless steel (k = 15 W / [m ° C]). The temperature of the inner surface is maintained at 150 ° C, and the outer surface is 30 ° C. At constant conditions and there is no heat generation from the pipe, calculate the heat transfer rate that occurs in the pipe wall. = Answer watt.
A 2-m * 1.5-m section of wall of an industrial furnaceburning natural gas is not insulated, and the temperatureat the outer surface of this section is measured to be 80°C.The temperature of the furnace room is 30°C, and the combinedconvection and radiation heat transfer coefficient at thesurface of the outer furnace is 10 W/m2·K. It is proposed toinsulate this section of the furnace wall with glass wool insulation(k = 0.038 W/m·K) in order to reduce the heat lossby 90 percent. Assuming the outer surface temperature ofthe metal section still remains at about 110°C, determine thethickness of the insulation that needs to be used.The furnace operates continuously and has an efficiency of78 percent. The price of the natural gas is $1.10/therm (1 therm =105,500 kJ of energy content). If the installation of the insulationwill cost $250 for materials and labor, determine how long it willtake for the insulation to pay for itself from the energy it saves.
As a rough approximation, the human body may be considered to be a cylinder of length L=2.0m and circumference C=0.8m. (To simplify things, ignore the circular top and bottom of the cylinder, and just consider the cylindrical sides.) If the emissivity of skin is taken to be e=0.6, and the surface temperature is taken to be T=30∘C, how much thermal power P does the human body radiate?