An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 3.4, Problem 29P
Sketch a qualitatively accurate graph of the entropy of a substance (perhaps
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Hi, could I get some help with this macro-connection physics problem involving isothermal expansion?
The set up is:
For an isothermal reversible expansion of two moles of an ideal gas, what is the entropy change of the a) gas and b) the surroundings in J/K to 4 digits of precision if the gas volume quadruples, assuming NA = 6.022e23 and kB = 1.38e-23 J/K?
Thank you.
Starting with the Clausius Inequality, ∂S ≥ ∂q/T, can you prove that, under conditions of constant pressure and entropy, for the total entropy to increase, ∂H ≤ 0 J?
Polymers, like rubber, are made of very long molecules, usually tangled up in a configuration that has lots of entropy. As a very crude model of a rubber band, consider a chain of N links, each of length L Imagine that each link has only two possible states, pointing either left or right. The total length L of the rubber band is the net displacement from the beginning of the first link to the end of the last link.
Using the thermodynamic identity, you can now express the tension force F in terms of a partial derivative of the entropy. From this expression, compute the tension in terms of L, T , N, and l.
Chapter 3 Solutions
An Introduction to Thermal Physics
Ch. 3.1 - Use Table 3.1 to compute the temperature of solid...Ch. 3.1 - Use the definition of temperature to prove the...Ch. 3.1 - Figure 3.3 shows graphs of entropy vs. energy for...Ch. 3.1 - Can a miserly system, with a concave-up...Ch. 3.1 - Prob. 5PCh. 3.1 - Prob. 6PCh. 3.1 - Prob. 7PCh. 3.2 - Prob. 8PCh. 3.2 - In solid carbon monoxide, each CO molecule has two...Ch. 3.2 - An ice cube (mass 30 g) at 0C is left sitting on...
Ch. 3.2 - In order to take a nice warm bath, you mix 50...Ch. 3.2 - Estimate the change in the entropy of the universe...Ch. 3.2 - When the sun is high in the sky, it delivers...Ch. 3.2 - Experimental measurements of the heat capacity of...Ch. 3.2 - Prob. 15PCh. 3.2 - A bit of computer memory is some physical object...Ch. 3.3 - Prob. 17PCh. 3.3 - Prob. 18PCh. 3.3 - Prob. 19PCh. 3.3 - Prob. 20PCh. 3.3 - Prob. 21PCh. 3.3 - Prob. 22PCh. 3.3 - Prob. 23PCh. 3.3 - Prob. 24PCh. 3.3 - Prob. 25PCh. 3.3 - Prob. 26PCh. 3.4 - What partial-derivative relation can you derive...Ch. 3.4 - A liter of air, initially at room temperature and...Ch. 3.4 - Sketch a qualitatively accurate graph of the...Ch. 3.4 - As shown in Figure 1.14, the heat capacity of...Ch. 3.4 - Experimental measurements of heat capacities are...Ch. 3.4 - A cylinder contains one liter of air at room...Ch. 3.4 - Prob. 33PCh. 3.4 - Polymers, like rubber, are made of very long...Ch. 3.5 - Prob. 35PCh. 3.5 - Prob. 36PCh. 3.5 - Prob. 37PCh. 3.5 - Suppose you have a mixture of gases (such as air,...Ch. 3.6 - Prob. 39P
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- A cylinder contains 500 g of helium at 120 atm and 20 . The valve is leaky, and all the gas slowly escapes isothermally into the atmosphere. Use the results of the preceding problem to determine the resulting change in entropy of the universe.arrow_forwardWhat can be said about the total entropy of the universe? Why is it true?arrow_forwardAn ideal gas at temperature T is stored in the left half of an insulating container of volume V using a partition of negligible volume (see below). What is the entropy change per mole of the gas in each of the following cases? (a) The partition is suddenly removed and the gas quickly fills the entire container. (b) A tiny hole is punctured in the partition and after a long period, the gas reaches an equilibrium state such that there is no net flow through the hole. (c) The partition is moved very slowly and adiabatically all the way to the light wall so that the gas finally fills the entire container.arrow_forward
- A monoatomic ideal gas (n moles) goes through a cyclic process shown below. Find the change in entropy of the gas in each step and the total entropy change over the entire cycle.arrow_forwardA great deal of effort, time, and money has been spent in the quest for a so-called perpetual-motion machine, which is defined as a hypothetical machine that operates or produces useful work indefinitely and/or a hypothetical machine that produces mole work or energy than it consumes. Explain, in terms of the first law of thermodynamics, why or why not such a machine is likely to be constructed.arrow_forwardWhich of the following thermodynamic quantities is not a state function? Explain. a. work b. entropy c. enthalpy d. free energyarrow_forward
- I attached the question and the answer How does the negative sign appear in the first integral And then what are they doing in the second part what’s env ? Shouldn’t we just find the total change in entropyarrow_forwardIn Debye Approximation the entropy at some temperature T (less than 10 K) is aT(Blank 1 ) /3 If the value of this entropy at T = 3.5 K is 1.55 J / K , then the value of the coefficient "a" is : ( Blank 2)arrow_forwardFor one component gas that is confined in a box with volume V. V We can get the entropy of the gas as S = Nk, In where N is the total number of atoms, a is the radius of the atom. Can you guess (or work out) how it is obtained?arrow_forward
- Consider the reaction represented below, which is spontaneous at 298K SO2(g) + 2 NH3(g) → SO(NH2)2 (s) + H2O(l) ΔH° = -205 kJ 1. For the reaction, indicate whether the standard entropy change, ΔS° is positive, or negative, or zero. Justify your answer. 2. Which factor, the change in enthalpy or the change in entropy, provides the principal driving force for the reaction at 298 K? Explain.arrow_forwardUsing the information provided (image), compare the change in entropy during the isothermal expansion from 1 L to 2 L of one mole of a rigid diatomic ideal gas and one mole of a rigid diatomic Van der Waals gas with b = 0.08 L/mol (ethanol). Are the changes in entropy the same for both or is one greater than the other?arrow_forwardIn Figure all possible distributions and microstates are shown for four different particles shared between two boxes. Determine the entropy change, ΔS, if the particles are initially evenly distributed between the two boxes,but upon redistribution all end up in Box (b).arrow_forward
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