An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 4.3, Problem 18P
To determine
To Prove:The efficiency of Otto cycle is
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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.
Equations 6.92 and 6.93 (See attached) for the entropy and chemical potential involve the logarithm of the quantity V Zint!N vQ. Is this logarithm normally positive or negative? Plug in some numbers for an ordinary gas and discuss.
2.2
Consider a reversible process that takes an ideal gas
from an initial state a to a final equilibrium state b. Show that the
change in entropy of the gas is given by:
AS = nC, In ()+nR In ()
CL
Chapter 4 Solutions
An Introduction to Thermal Physics
Ch. 4.1 - Prob. 1PCh. 4.1 - At a power plant that produces 1 GW ( 109 watts)...Ch. 4.1 - A power plant produces 1 GW of electricity, at an...Ch. 4.1 - It has been proposed to use the thermal gradient...Ch. 4.1 - Prove directly (by calculating the heat taken in...Ch. 4.1 - To get more than an infinitesimal amount of work...Ch. 4.2 - Why must you put an air conditioner in the window...Ch. 4.2 - Can you cool off your kitchen by leaving the...Ch. 4.2 - Prob. 9PCh. 4.2 - Suppose that heat leaks into your kitchen...
Ch. 4.2 - What is the maximum possible COP for a cyclic...Ch. 4.2 - Explain why an ideal gas taken around a...Ch. 4.2 - Under many conditions, the rate at which heat...Ch. 4.2 - Prob. 14PCh. 4.2 - In an absorption refrigerator the energy driving...Ch. 4.2 - Prob. 16PCh. 4.2 - Prob. 17PCh. 4.3 - Prob. 18PCh. 4.3 - The amount of work done by each stroke of an...Ch. 4.3 - Derive a formula for the efficiency of the Diesel...Ch. 4.3 - The ingenious Stirling engine is a true heat...Ch. 4.3 - A small-scale steam engine might operate between...Ch. 4.3 - Prob. 23PCh. 4.3 - Calculate the efficiency of a Rankine cycle that...Ch. 4.3 - In a real turbine, the entropy of the steam will...Ch. 4.3 - A coal-fired power plant, with parameters similar...Ch. 4.3 - In Table 4.1, why does the entropy of water...Ch. 4.3 - Imagine that your dog has eaten the portion of...Ch. 4.4 - Liquid HFC-134a at its boiling point at 12 bars...Ch. 4.4 - Consider a household refrigerator that uses...Ch. 4.4 - Suppose that the throttling valve in the...Ch. 4.4 - Suppose you are told to design a household air...Ch. 4.4 - Prob. 33PCh. 4.4 - Consider an ideal Hampson-Linde cycle in which no...Ch. 4.4 - The magnetic field created by a dipole has a...Ch. 4.4 - Prob. 36PCh. 4.4 - A common (but imprecise) way of stating the third...
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- Problem 1: Describe a situation in which the entropy of a container of gas is constant. In other words, come up with your own problem where the answer is that AS = 0.arrow_forwardI 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.arrow_forwardThermodynamics Answer the following with complete solutions. write legibly. A Carnot engine has an efficiency of 30%. Its efficiency is to be increased to 50%. By what must the temperature of the source be increased if the sink is at 300 K?arrow_forward
- 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.arrow_forwardProblem #2 For heat exchange between a thermal reservoir at 300 K and a constant volume system containing one mole of monatomic ideal gas: a) Derive the equation for the total change in entropy for a designed initial system temperature Tj. b) Plot AStotal vs. Tsys for the initial system temperature ranging from 160 K to 500 K in increments of 10 K (i.e., Tsys = 160 K, 170 K, ... , 500 K). Use Matlab, Excel or similar plotting software for your plot. Label the plot axes and include units. %Darrow_forwardCalculate the efficiency of the Carnot engine for ideal gas. Consider the figure below for a complete cycle of Carnot engine, where the cycle goes back from ad->ab->bc->cd Please answer the blanks below. Answer until QC. Part 1/2arrow_forward
- 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.arrow_forwardplease do fast 5. Find the expression for the entropy of a single harmonic oscillator.arrow_forwardAt steady state, a thermodynamic cycle operating between hot and cold reservoirs at 1000 K and 500 K, respectively, receives energy by heat transfer from the hot reservoir at a rate of 1500 kW, discharges energy by heat transfer to the cold reservoir, and develops power at a rate of (a) 1000 kW, (b) 750 kW, (c) 0 kW. For each case, apply Eq. 5.13 on a time- rate basis to determine whether the cycle operates reversibly, operates irreversibly, or is impossible.arrow_forward
- The attached images have 3 parts, solve those 3 parts and also because of limited images to upload, this is the 4th part, iam typing here: Calculate the total change in entropy for entire system, in J/K.arrow_forwarda. 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.arrow_forwardProblem (5.1): Consider a steam power plant that operates on a simple ideal Rankine cycle and has a net power output of 45 MW. Steam enters the turbine at 7 MPa and 500°C and is cooled in the condenser at a pressure of 10 kPa by running cooling water from a lake through the tubes of the condenser. Show the cycle on a (T-S) diagram with respect to the saturation lines, and determine (a) the thermal efficiency of the cycle (b) the mass flow rat r i? steam. Ans. (38.9%, 36 kg/s)arrow_forward
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