3. The entropy of an ideal gas is S = Nkg In V. Entropy is a state function rather than a pathfunction, and in this problem, you will show an example of the entropy change for an ideal gasbeing the same when you go between the same two states by two different pathways.A. Express ASV = S2 (V2) - S₁(V1), the change in entropy upon changing the volume from V₁toV2, at fixed particle number N and energy, U.B. Express ASN = S₂(N₂) - S₁ (N₁), the change in entropy upon changing the particle numberfrom N₁ to N2, at fixed volume V and energy U.C. Write an expression for the entropy change, AS, for a two-step process (V₁, N₁) →(V2, N₁) → (V2, N₂) in which the volume changes first at fixed particle number, then the particlenumber changes at fixed volume. Again, assume energy is constant. D. Show that the change in entropy, AS, above is exactly the same as for the two-step processin reverse order: change the particle number first, then the volume.

Solution for Part D: Showing Entropy Change is the Same in Reverse OrderWe need to show that the…

Answered: 3. The entropy of an ideal gas is S =…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter22: Entropy And The Second Law Of Thermodynamics

Section: Chapter Questions

Problem 68PQ

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A power plant has been proposed that would make use of the temperature gradient in the ocean. The system is to operate between 20.0C (surface water temperature) and 5.00C (water temperature at a depth of about 1 km). (a) What is the maximum efficiency of such a system? (b) If the useful power output of the plant is 75.0 MW, how much energy is absorbed per hour? (c) In view of your answer to part (a), do you think such a system is worthwhile (considering that there is no charge for fuel)?
Assume a sample of an ideal gas is at room temperature. What action will necessarily make the entropy of the sample increase? (a) Transfer energy into it by heat, (b) Transfer energy into it irreversibly by heat, (c) Do work on it. (d) Increase either its temperature or its volume, without letting the other variable decrease, (e) None of those choices is correct.
(a) Prepare a table like Table 18.1 for the following occurrence. You toss four coins into the air simultaneously and then record the results of your tosses in terms of the numbers of heads (H) and tails (T) that result. For example, HHTH and HTHH are two possible ways in which three heads and one tail can be achieved. (b) On the basis of your table, what is the most probable result recorded for a toss? In terms of entropy, (c) what is the most ordered macrostate, and (d) what is the most disordered?
(a) Construct a table showing the macro states and all of the individual microstates for tossing 13 coins. (Use Table 15.5 as a guide.) (b) How many macro states are there? (c) What is the total number of microstates? (d) What percent chance is here of tossing 5 heads and 1 tail? (e) How much more likely are you to toss 3 heads and 3 tails than 5 heads and 1 tail? (Take me ratio of the number of microstates to find out.)
A triple-point cell such as the one shown in Figure 19.20 (page 571) is constructed and calibrated at sea level. It is then shipped to Denver, which is 1 mi above sea level. Can the researchers in the Denver lab use the triple-point cell just as in a laboratory at sea level, or will special adjustments be needed? Explain.
(a) How much food energy will a man metabolize in the process of doing 35.0 kJ of work with an efficiency of 5.00%? (b) How much heal transfer occurs to the environment to keep his temperature constant? Explicitly show how you follow the steps in the Problem—Solving Strategy for thermodynamics found in Problem-Solving Strategies for Thermodynamics.
(a) What is the change in entropy if you start with 100 coins in the 45 heads and 55 tails macrostate, toss them, and get 51 heads and 49 tails? (b) What if you get 75 heads and 25 tails? (c) How much more likely is 51 heads and 49 tails than 75 heads and 25 tails? (d) Dues either outcome violate the second law of thermodynamics?
(a) If you toss 10 coins, what percent of the time will you get the three most likely macrostates (6 heads and 4 tails, 5 heads and 5 tails, 4 heads and 6 tails)? (b) You can realistically toss 10 coins and count the number of heads and tails about twice a minute. At mat rate, how long will it take on average to get either 10 heads and 0 tails or 0 heads and 10 tails?
What is the entropy of a freshly shuffled deck of 52 playing cards?
(a) What is the change in entropy if you start with 10 coins in the 5 heads and 5 tails macrostate, toss them, and get 2 heads and 8 tails? (b) How much more likely is 5 heads and 5 tails than 2 heads and 8 tails? (Take the ratio of the number of microstates to find out.) (c) If you were betting on 2 heads and 8 tails would you accept odds of 252 to 45? Explain Why or why not. Table 15.5 10Coin Toss MacrostateNumber of Microstates (W) Heads Tails 10 0 1 9 1 10 8 2 45 7 3 120 6 4 210 5 5 252 4 6 210 3 7 120 2 8 45 1 9 10 0 10 1 Total: 1024
Objects A and B with TA TB are placed in thermal contact and come to equilibrium. (a) For which object does the entropy increase? (b) For which object does the entropy decrease? (c) Which object has the greater magnitude of entropy change?
An engine with an efficiency of 0.36 can supply a power of 140 hp. At what rate does it exhaust heat to the environment? Express your answer in watts.

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