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Check Your Understanding A quantity of heat Q is absorbed from a reservoir at a temperature T h by a cooler reservoir at a temperature T c . What is the entropy change of the hot reservoir, the cold reservoir, and the universe?

Q / T h ; Q / T c ; and Q ( T h T c ) / ( T h T c )

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Check Your Understanding A 50-g copper piece at a temperature of 20 °C is placed into a large insulated vat of water at 100 °C . (a) What is the entropy change of the copper piece when it reaches thermal equilibrium with the water? (b) What is the entropy change of the water? (c) What is the entropy change of the universe?

a. 4.71 J/K; b. −4.18 J/K; c. 0.53 J/K

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View this site to learn about entropy and microstates. Start with a large barrier in the middle and 1000 molecules in only the left chamber. What is the total entropy of the system? Now remove the barrier and let the molecules travel from the left to the right hand side? What is the total entropy of the system now? Lastly, add heat and note what happens to the temperature. Did this increase entropy of the system?

Summary

  • Entropy can be related to how disordered a system is—the more it is disordered, the higher is its entropy. In any irreversible process, the universe becomes more disordered.
  • According to the third law of thermodynamics, absolute zero temperature is unreachable.

Key equations

Result of energy conservation W = Q h Q c
Efficiency of a heat engine e = W Q h = 1 Q c Q h
Coefficient of performance of a refrigerator K R = Q c W = Q c Q h Q c
Coefficient of performance of a heat pump K P = Q h W = Q h Q h Q c
Resulting efficiency of a Carnot cycle e = 1 T c T h
Performance coefficient of a reversible refrigerator K R = T c T h T c
Performance coefficient of a reversible heat pump K P = T h T h T c
Entropy of a system undergoing a reversible process at a constant temperature Δ S = Q T
Change of entropy of a system under a reversible process Δ S = S B S A = A B d Q / T
Entropy of a system undergoing any complete reversible cyclic process d S = d Q T = 0
Change of entropy of a closed system under an irreversible process Δ S 0
Change in entropy of the system along an isotherm lim T 0 ( Δ S ) T = 0

Conceptual questions

Are the entropy changes of the systems in the following processes positive or negative? (a) water vapor that condenses on a cold surface; (b) gas in a container that leaks into the surrounding atmosphere; (c) an ice cube that melts in a glass of lukewarm water; (d) the lukewarm water of part (c); (e) a real heat engine performing a cycle; (f) food cooled in a refrigerator.

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Discuss the entropy changes in the systems of Question 21.10 in terms of disorder.

Entropy is a function of disorder, so all the answers apply here as well.

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Problems

A copper rod of cross-sectional area 5.0 cm 2 and length 5.0 m conducts heat from a heat reservoir at 373 K to one at 273 K. What is the time rate of change of the universe’s entropy for this process?

3.78 × 10 −3 W/K

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Fifty grams of water at 20 °C is heated until it becomes vapor at 100 °C . Calculate the change in entropy of the water in this process.

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Fifty grams of water at 0 °C are changed into vapor at 100 °C . What is the change in entropy of the water in this process?

430 J/K

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Questions & Answers

Maxwell's stress tensor is
Ami Reply
if 6.0×10^13 electrons are placed on a metal sphere of charge 9.0micro Coulombs, what is the net charge on the sphere
Rita Reply
18.51micro Coulombs
ASHOK
Is it possible to find the magnetic field of a circular loop at the centre by using ampere's law?
Rb Reply
Is it possible to find the magnetic field of a circular loop at it's centre?
Rb Reply
yes
Brother
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
Gifty Reply
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
Gifty
what is electrostatics
Yakub Reply
Study of charges which are at rest
himanshu
Explain Kinematics
Glory Reply
Two equal positive charges are repelling each other. The force on the charge on the left is 3.0 Newtons. Using your notes on Coulomb's law, and the forces acting on each of the charges, what is the force on the charge on the right?
Nya Reply
Using the same two positive charges, the left positive charge is increased so that its charge is 4 times LARGER than the charge on the right. Using your notes on Coulomb's law and changes to the charge, once the charge is increased, what is the new force of repulsion between the two positive charges?
Nya
A mass 'm' is attached to a spring oscillates every 5 second. If the mass is increased by a 5 kg, the period increases by 3 second. Find its initial mass 'm'
Md Reply
a hot water tank containing 50,000g of water is heated by an electric immersion heater rated at 3kilowatt,240volt, calculate the current
Samuel Reply
what is charge
Aamir Reply
product of current and time
Jaffar
Why always amber gain electrons and fur loose electrons? Why the opposite doesn't happen?
Mohammed Reply
A closely wound search coil has an area of 4cm^2,1000 turns and a resistance of 40ohm. It is connected to a ballistic galvanometer whose resistance is 24 ohm. When coil is rotated from a position parallel to uniform magnetic field to one perpendicular to field,the galvanometer indicates a charge
Palak Reply
Using Kirchhoff's rules, when choosing your loops, can you choose a loop that doesn't have a voltage?
Michael Reply
how was the check your understand 12.7 solved?
Bysteria Reply
Practice Key Terms 3

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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