Your calculator can't handle enormous exponents, but we canmake sense of large powers of e by converting them to largepowers of 10. If we write e = 10%, then eß = (10°)³ = 10³.Part AWhat is the value of a?απ17 ΑΣΦSubmitPart BRequest AnswerWhat is the multiplicity of a macrostate with entropy S = 1.0 J/K? Give your answer as a power of 10.Ω = 10αβ; αβ==)Π| ΑΣΦ

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Your calculator can't handle enormous exponents, but we can make sense of large powers of e by converting them to large powers of 10. If we write e = 10°, then e = (10°)³ = 108. ▼ Part A What is the value of a? α = Submit Part B ΕΠΙ ΑΣΦ Request Answer What is the multiplicity of a macrostate with entropy S = 1.0 J/K? Give your answer as a power of 10. Ω = 10^β, αβ= ΠΫΠΙ ΑΣΦ ? 3 ?

Your calculator can't handle enormous exponents, but we can make sense of large powers of e by converting them to large powers of 10. If we write e = 10°, then e = (10°)³ = 108. ▼ Part A What is the value of a? α = Submit Part B ΕΠΙ ΑΣΦ Request Answer What is the multiplicity of a macrostate with entropy S = 1.0 J/K? Give your answer as a power of 10. Ω = 10^β, αβ= ΠΫΠΙ ΑΣΦ ? 3 ?

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter2: The Kinetic Theory Of Gases

Section: Chapter Questions

Problem 69P: By counting squares in the following figure, estimate the fraction of argon atoms at T = 300 K that...

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Now, let's use this property of logarithms to learn something about the number of microstates available to a molecular system. The absolute entropy of a system is related to the number of microstates available to it via Boltzmann's formula S = kB In W. If a system containing one mole of an ideal gas has an entropy of 167.7 J/K, how many microstates does it have? Report the order of W, as we have defined it above, and you should use scientific notation, 1.23E45, and report 3 (three) significant figures.
One kilogram of water at 0C is heated to 100C. Compute its change in entropy. Assume that the specific heat of water is constant at 4190 J/kg . K over this temperature range.
100 g of water at 0 C (degrees Celsius) is heated to 100 C. Compute its change in entropy.
For either a monatomic ideal gas or a high-temperature Einstein solid, the entropy is given by Nk times some logarithm. The logarithm is never large, so if all you want is an order-of-magnitude estimate, you can neglect it and just say S - Nk. That is, the entropy in fundamental units is of the order of the rv number of particles in the system. This conclusion turns out to be true for most systems (with some important exceptions at low temperatures where the particles are behaving in an orderly way). So just for fun, make a very rough estimate of the entropy of each of the following: this book (a kilogram of carbon compounds); a moose (400 kg of water); the sun (2 x 1030 kg of ionized hydrogen).
For one component gas that is confined in a box with volume V. We can get the entropy of the gas as S= Nk, in- where N is the total a² number of atoms, a is the radius of the atom. Can you guess how it is obtained?
a. Find an appropriate expression for the change in entropy in the following two cases: 1) S=S(T, V) 2) s= S(T, P) Where: S is entropy, T is temperature, V is volume, P is pressure b. Prove the following two themodynamie property relationships (똥),-() 8C, Where: T, P. V are temperature, pressure and volume, respectively. C, and C, are specific heats at constant volume and constant pressure, respectively.
I have answered b but I got 4.33 Kg for A and not correct (a) What is the entropy of an Einstein solid with 4 atoms and an energy of 18ε? Express your answer as a multiple of kB . The entropy of the solid is ______ kB.(b) What is the entropy of an Einstein solid in a macropartition that contains 9 ×10 e690 microstates? Express your answer as a multiple of kB. The entropy of the solid is 1590.92kB.
A highly non-ideal gas has an entropy given by S=aNU/V, where the internal energy, U is a function of T.Find the pressure, the expression for the heat capacity at constant volume, and the chemical potential.
A container of neon gas has the following properties: (1) 2.4 moles (2) T = 400 K (3) p = 0.8 atm. Calculate the entropy in J K-1 as a number in normal form accurate to 1 decimal place (X.X or XX.X, etc.). Do not include units in your answer. USE THE EXACT METHOD IN THE PICTURE BELOW, JUST SUB IN THE NEW VALUES IN THE QURSTION AND REPLACE THEM IN THE IMAGE PROVIDED.
One way to "derive" the thermodynamic definition for entropy is simply to recognize that its thermodynamic definition must be a state function, and all thermodynamic state functions are worthy of giving a special name and carry special meaning. a) Starting with the First Law of Thermodynamics (expressed either of 2 ways) AU = q + w du = dq + dw show all the steps and assumptions/conditions required to arrive at the new expression below, which includes the definition of entropy: AS - arev AU T T - nRln () arev must be state function. b) Using your result from part (a), explain why T To be explicit, explain why entropy must defined by (P, V, T) alone, and any change between the same 2 states, (P₁, V₁, T₁). and (P2, V2, T2), regardless of path, will give the same change in entropy.
Two kilograms of water at 0 degree Celsius is heated to 100 degree Celsius. Compute its entropy in change. The temperature of the water is increased reversibly in a series of infinitesimal steps, in each of which the temperature is raised by an infinitesimal amount dT. The heat required is dQ =mc dT
Please answer the following question(s): 1. (a) What is the best coefficient of performance for a refrigerator that cools an environment at -28° C and has heat transfer to another environment at 47 ° C? COP ref (b) How much work must be done for a heat transfer of 4186 kJ from the cold environment? W = kj (c) What is the cost of doing this if the work costs 10.0 cents per 3.6 × 106 J (a kilowatt-hour)? Cost in cents = ✓ (d) How many kJ of heat transfer, Qh occurs into the warm environment? Qh= kj Think about what type of refrigerator might operate between these temperatures. Hint: Use the appropriate formula for a refrigerator which is different from a heat pump.