An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 1.6, Problem 45P
(a)
To determine
To Write:The term w purely in terms of x and z, and then in terms ofy and z.
(b)
To determine
The partial derivatives of
(c)
To determine
The remaining four partial derivatives of w.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Which of the following statements is true
Select one:
O " ("f(x, y)dxdy gives the area of the graph of f(x. y) above a rectangular region in xy-plane.
O If f(x, v. 2) = x² + y? - - xyz + 2. then f(x, y. z) =f(2. y. x),
O if f(x, y, 2) = x² + y² - z? - xyz + 2, then f(x. y. ) = f(.x.2)
O If f(x, y) is constant functionof y, then = 0
(a) Find the scalar products î · î, ĵ· ĵ, and k · Ê.
(b) Find î · ĵ, ĵ · k, and k · î
(c) Use the distributive law to multiply out the scalar product of two arbitrary vectors Ã
Axî + Ayî + A¸k and B
Equation 6.4.
Bxî + Byĵ + Bzk, and use the results of (a) and (b) to verify
Find a unit vector in the same direction as the vector A = 4i−2j+ 4k, and another unit vector in the same direction as B = −4i + 3k. Show that the vector sum of these unit vectors bisects the angle between A and B. Hint: Sketch the rhombus having the two unit vectors as adjacent sides.
Chapter 1 Solutions
An Introduction to Thermal Physics
Ch. 1.1 - Prob. 1PCh. 1.1 - The Rankine temperature scale (abbreviatedR) uses...Ch. 1.1 - Prob. 3PCh. 1.1 - Does it ever make sense to say that one object is...Ch. 1.1 - Prob. 5PCh. 1.1 - Give an example to illustrate why you cannot...Ch. 1.1 - Prob. 7PCh. 1.1 - For a solid, we also define the linear thermal...Ch. 1.2 - What is the volume of one mole of air, at room...Ch. 1.2 - Energy in Thermal Physics Estimate the number of...
Ch. 1.2 - Rooms A and B are the same size, and are connected...Ch. 1.2 - Calculate the average volume per molecule for an...Ch. 1.2 - A mole is approximately the number of protons in a...Ch. 1.2 - Calculate the mass of a mole of dry air, which is...Ch. 1.2 - Estimate the average temperature of the air inside...Ch. 1.2 - Prob. 16PCh. 1.2 - Prob. 17PCh. 1.2 - Prob. 18PCh. 1.2 - Suppose you have a gas containing hydrogen...Ch. 1.2 - Prob. 20PCh. 1.2 - During a hailstorm, hailstones with an average...Ch. 1.2 - Prob. 22PCh. 1.3 - Calculate the total thermal energy in a liter of...Ch. 1.3 - Calculate the total thermal energy in a gram of...Ch. 1.3 - List all the degrees of freedom, or as many as you...Ch. 1.4 - A battery is connected in series to a resistor,...Ch. 1.4 - Give an example of a process in which no heat is...Ch. 1.4 - Estimate how long it should take to bring a cup of...Ch. 1.4 - A cup containing 200 g of water is sitting on your...Ch. 1.4 - Put a few spoonfuls of water into a bottle with a...Ch. 1.5 - Imagine some helium in cylinder with an initial...Ch. 1.5 - Prob. 32PCh. 1.5 - An ideal gas is made to undergo the cyclic process...Ch. 1.5 - An ideal diatomic gas, in a cylinder with a...Ch. 1.5 - Prob. 35PCh. 1.5 - In the course of pumping up a bicycle tire, a...Ch. 1.5 - Prob. 37PCh. 1.5 - Two identical bubbles of gas form at the bottom of...Ch. 1.5 - By applying Newtons laws to the oscillations of a...Ch. 1.5 - In problem 1.16 you calculated the pressure of...Ch. 1.6 - To measure the heat capacity of an object, all you...Ch. 1.6 - The specific heat capacity of Albertsons Rotini...Ch. 1.6 - Calculate the heat capacity of liquid water per...Ch. 1.6 - Prob. 44PCh. 1.6 - Prob. 45PCh. 1.6 - Measured heat capacities of solids and liquids are...Ch. 1.6 - Your 200-g cup of tea is boiling-hot. About how...Ch. 1.6 - When spring finally arrives in the mountains, the...Ch. 1.6 - Prob. 49PCh. 1.6 - Consider the combustion of one mole of methane...Ch. 1.6 - Use the data at the back of this book to determine...Ch. 1.6 - The enthalpy of combustion of a gallon (3.8...Ch. 1.6 - Look up the enthalpy of formation of atomic...Ch. 1.6 - Prob. 54PCh. 1.6 - Heat capacities are normally positive, but there...Ch. 1.7 - Calculate the rate of heat conduction through a...Ch. 1.7 - Home owners and builders discuss thermal...Ch. 1.7 - According to a standard reference table, the R...Ch. 1.7 - Make a rough estimate of the total rate or...Ch. 1.7 - A frying pan is quickly heated on the stovetop to...Ch. 1.7 - Geologists measure conductive heat flow out of the...Ch. 1.7 - Consider a uniform rod of material whose...Ch. 1.7 - Prob. 63PCh. 1.7 - Make a rough estimate of the thermal conductivity...Ch. 1.7 - Prob. 65PCh. 1.7 - In analogy with the thermal conductivity, derive...Ch. 1.7 - Make a rough estimate of how far food coloring (or...Ch. 1.7 - Prob. 68PCh. 1.7 - Imagine a narrow pipe, filled with fluid, in which...Ch. 1.7 - Prob. 70P
Knowledge Booster
Similar questions
- Question 1.1: Calculate the dot product of vectors A and B, where JA|=5 and |B|=3 and EXPLAIN. А B a.arrow_forward(a) Let r = (x, Y, z) and r = ||r||. Assuming r cannot equal 0, is there a value of p for which the vector field f(r)=r/r^P is solenoidal? You must fully justify your answer. (b) Show that if f and g are twice differentiable scalar fields then V²(f g) = ƒ V^2g+ g V²f + 2Vƒ · Vgarrow_forwardGiven P = 32 u, 90° N of E and R = 12 u, 45° N of E, find P - R in unit-vector form. Use the component method.arrow_forward
- The θ integration fails if α is non-constant. There is also a type of situation where the step before the integration fails, involving ω. Question 1: derive ω = αt + ω0. Start with the derivatives I began with, and derive this equation. Question 2: derive θ = 1/2αt2 + ω0t + θ0. You may use prior derived results. Question 3: derive θ = θ0 + (ω + ω0) t/2. You probably need to use prior derived results.arrow_forwardProblem no 1: Find sum, difference and scalar and vetor product of vectors u=[−4,6],w=[0,4]. Draw and calculate.arrow_forwardFor the pair of vectors A = (6.00î + 4.00ĵ) and B = (9.0oî – 6.00ĵ) in the xy plane, determine the following. (Enter all angle answers between 0 and 180°.) %3D (a) The scalar product A: B = (b) The angle 0 between the vectors (c) The angles a and ß which are respectively the (smallest) angles between the vector A and the positive x and positive y axes a = %D (d) The angles y and 8, which are respectively the (smallest) angles between the vector B and the positive x and positive y axes Y 8 %3Darrow_forward
- For any arbitrary vectors u, v and w, prove thatarrow_forwardconsider x place as P. solve this problems correctly.arrow_forwardOur unforced spring mass model is mx00 + βx0 + kx = 0 with m, β, k >0. We know physically that our spring will eventually come to rest nomatter the initial conditions or the values of m, β, or k. If our modelis a good model, all solutions x(t) should approach 0 as t → ∞. Foreach of the three cases below, explain how we know that both rootsr1,2 =−β ± Sqrt(β^2 − 4km)/2mwill lead to solutions that exhibit exponentialdecay.(a) β^2 − 4km > 0. (b) β^2 − 4km =0. (c) β^2 − 4km >= 0.arrow_forward
- Let vectors A=(2,1,−4), B=(−3,0,1), and C=(−1,−1,2).Calculate the following: What is the angle θAB between A and B?arrow_forwardGiven the vectors A = -5i - 3j - 8k ; B = 4i - 2j + 3k ; C = 10i -12j - 8k a. Find A x B b. Evaluate the mixed triple products A . (B x C) c. Find : A x (A x B)arrow_forwardFind the scalar and vector products of two vectors. a = (3iˆ – 4jˆ + 5ˆk )and b = (– 2iˆ + jˆ – 3ˆ k ).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- 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
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON