A Styrofoam cup holding 130 g of hot water at 97°C cools to room temperature, 23.0°C. What is the change in entropy of the room? Neglect the specific heat of the cup and any change in temperature of the room. J/K

A Styrofoam cup holding 130 g of hot water at 97°C cools to room temperature, 23.0°C. What is the change in entropy of the room? Neglect the specific heat of the cup and any change in temperature of the room. J/K

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter18: Heat Engines, Entropy, And The Second Law Of Thermodynamics

Section: Chapter Questions

Problem 33P

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(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 65-g ice cube is initially at 0.0C. (a) Find the change in entropy of the cube after it melts completely at 0.0C. (b) What is the change in entropy of the environment in this process? Hint: The latent heat of fusion for water is 3.33 105 J/kg.
(a) How much heat transfer occurs from 20.0 kg of 90.0C water placed in contact with 20.0 kg of 10.0C water, producing a final temperature of 50.0C ? (b) How much work could a Carnot engine do with this heat transfer, assuming it operates between two reservoirs at constant temperatures of 90.0C and 10.0C ? (c) What increase in entropy is produced by mixing 20.0 kg of 90.0C water with 20.0 kg of 10.0C water? (d) Calculate the amount of work made unavailable by this mixing using a low temperature of 10.0C, and compare it with the work done by the Garnet engine. Explicitly show how you follow the steps in the Problem-Solving Strategies for Entropy. (e) Discuss how everyday processes make increasingly more energy unavailable to do work, as implied by this problem.
(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
A sample of a monatomic ideal gas is contained in a cylinder with a piston. Its state is represented by the dot in the PV diagram shown in Figure OQ18.9. Arrows A through E represent isobaric, isothermal, adiabatic, and isovolumetric processes that the sample can undergo. In each process except D, the volume changes by a factor of 2. All five processes are reversible. Rank the processes according to the change in entropy of the gas from the largest positive value to the largest-magnitude negative value. In your rankings, display any cases of equality. Figure OQ18.9
(a) On a winter day, a certain house loses 5.00108J of heat to the outside (about 500,000 Btu). What is the total change in entropy due to this heat transfer alone, assuming an average indoor temperature of 21.0C and an average outdoor temperature of 5.00C ? (b) This large change in entropy implies a large amount of energy has become unavailable to do work. Where do we find more energy when such energy is lost to us?
A system consisting of n moles of an ideal gas with molar specific heat at constant pressure Cr undergoes two reversible processes. It starts with pressure Pi and volume Vi, expands isothermally, and then contracts adiabatically to reach a final state with pressure Pi and volume 3Vi. (a) Find its change in entropy in the isothermal process. (The entropy does not change in the adiabatic process.) (b) What If? Explain why the answer to part (a) must be the same as the answer to Problem 46. (You do not need to solve Problem 46 to answer this question.)
(a) In reaching equilibrium, how much heat transfer occurs from 1.00 kg of water at 40.0C when it is placed in contact with 1.00 kg of 20.0C water in reaching equilibrium? (b) What is the change in entropy due to this heat transfer? (c) How much work is made unavailable, taking the lowest temperature to be 20.0C ? Explicitly show how you follow the steps in the Problem-Solving Strategies for Entropy.
Explain how water’s entropy can decrease when it freezes without violating the second law of thermodynamics. Specifically, explain what happens to the entropy of its surroundings.
Explain why a building made of bricks has smaller entropy than the same bricks in a disorganized pile. Do this by considering the number of ways that each could be formed (the number of microstates in each macrostate).
An ideal gas is taken from an initial temperature Ti to a higher final temperature Tf along two different reversible paths. Path A is at constant pressure, and path B is at constant volume. What is the relation between the entropy changes of the gas for these paths? (a) SA SB (b) SA = SB (c) SA SB
A biology laboratory is maintained at a constant temperature of 7.00C by an air conditioner, which is vented to the air outside. On a typical hot summer day, the outside temperature is 27.0C and the air-conditioning unit emits energy to the outside at a rate of 10.0 kW. Model the unit as having a coefficient of performance (COP) equal to 40.0% of the COP of an ideal Carnot device. (a) At what rate does the air conditioner remove energy from the laboratory? (b) Calculate the power required for the work input. (c) Find the change in entropy of the Universe produced by the air conditioner in 1.00 h. (d) What If? The outside temperature increases to 32.0C. Find the fractional change in the COP of the air conditioner.