# 4.7 Entropy on a microscopic scale  (Page 4/10)

 Page 4 / 10

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

$\text{−}Q\text{/}{T}_{\text{h}}$ ; $Q\text{/}{T}_{\text{c}}$ ; and $Q\left({T}_{\text{h}}-{T}_{\text{c}}\right)\text{/}\left({T}_{\text{h}}{T}_{\text{c}}\right)$

Check Your Understanding A 50-g copper piece at a temperature of $20\phantom{\rule{0.2em}{0ex}}\text{°C}$ is placed into a large insulated vat of water at $100\phantom{\rule{0.2em}{0ex}}\text{°C}$ . (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

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 $W={Q}_{\text{h}}-{Q}_{\text{c}}$ Efficiency of a heat engine $e=\frac{W}{{Q}_{\text{h}}}=1-\frac{{Q}_{\text{c}}}{{Q}_{\text{h}}}$ Coefficient of performance of a refrigerator ${K}_{\text{R}}=\frac{{Q}_{\text{c}}}{W}=\frac{{Q}_{\text{c}}}{{Q}_{\text{h}}-{Q}_{\text{c}}}$ Coefficient of performance of a heat pump ${K}_{\text{P}}=\frac{{Q}_{\text{h}}}{W}=\frac{{Q}_{\text{h}}}{{Q}_{\text{h}}-{Q}_{\text{c}}}$ Resulting efficiency of a Carnot cycle $e=1-\frac{{T}_{\text{c}}}{{T}_{\text{h}}}$ Performance coefficient of a reversible refrigerator ${K}_{\text{R}}=\frac{{T}_{\text{c}}}{{T}_{\text{h}}-{T}_{\text{c}}}$ Performance coefficient of a reversible heat pump ${K}_{\text{P}}=\frac{{T}_{\text{h}}}{{T}_{\text{h}}-{T}_{\text{c}}}$ Entropy of a system undergoing a reversible process at a constant temperature $\text{Δ}S=\frac{Q}{T}$ Change of entropy of a system under a reversible process $\text{Δ}S={S}_{B}-{S}_{A}={\int }_{A}^{B}dQ\text{/}T$ Entropy of a system undergoing any complete reversible cyclic process $\oint dS=\oint \frac{dQ}{T}=0$ Change of entropy of a closed system under an irreversible process $\text{Δ}S\ge 0$ Change in entropy of the system along an isotherm $\underset{T\to 0}{\text{lim}}{\left(\text{Δ}S\right)}_{T}=0$

## 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.

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.

## Problems

A copper rod of cross-sectional area $5.0\phantom{\rule{0.2em}{0ex}}{\text{cm}}^{2}$ 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?

$3.78\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-3}\phantom{\rule{0.2em}{0ex}}\text{W/K}$

Fifty grams of water at $20\phantom{\rule{0.2em}{0ex}}\text{°C}$ is heated until it becomes vapor at $100\phantom{\rule{0.2em}{0ex}}\text{°C}$ . Calculate the change in entropy of the water in this process.

Fifty grams of water at $0\phantom{\rule{0.2em}{0ex}}\text{°C}$ are changed into vapor at $100\phantom{\rule{0.2em}{0ex}}\text{°C}$ . What is the change in entropy of the water in this process?

430 J/K

what is calorimeter
heat measuring device
Suvransu
What is mean electric potential
Electric density formula
Int E•dA
Vineet
what is relation betweeen potential energy of a system and work done in bringing last chaege from infinity
Einstein and his general theory of relativity, a very nice concept,which revolutionize our modern world.
what's the theory of relativity?
Piyali
it related to universe time period
jyotirmayee
it is a theory in which time is taken as relative,for diff. motion of objects.
Antares
no !!!
jyotirmayee
it is E=mc'square
jyotirmayee
what is black hole?
jyotirmayee
E=mc^2 is just a reln which sums up everything dude
Antares
what does e=mc^2 stand for?explain
Piyali
m not dude
jyotirmayee
e for speed of light
jyotirmayee
c for speed of light
jyotirmayee
m for mass of object
jyotirmayee
black hole is a super massive object in space gravitation pull of which s so strong dt evn light cannot escape. John wheeler 1st detected it, n concept of it ws given by Einstein himself from his general theory of relativity. Basically v cn si 3 types of it super massive, interstellar n intermediate
Antares
which topic now u studying?
jyotirmayee
e defined? sorry it,s wrong
jyotirmayee
Why?
Arzoodan
how black holes r formed?
Piyali
e is not speed of light
jyotirmayee
black holes formed when the centre of very massive star collapsed itself
jyotirmayee
e is energy.
Antares
what do u mean by quantum mechanics?
jyotirmayee
in most of d cases black holes r formed by massive collapsed star or star system
Antares
sahoo u don't seem to understand relative physics, plz study that first.
Antares
exatly...
Arzoodan
Apollo is the name of a satellite !!!!!
jyotirmayee
quantum mechanics is d study of physics describing nature at d smallest level of energy of atoms n subatomic particles.
Antares
qm means explains about the microscopic particles..
KRANTHI
nope name of d sun god
Antares
why the mercury used in thermometers?
jyotirmayee
Ali brother ur exactly spelling is wrong,,,,,
jyotirmayee
why the colour of tube light white?
jyotirmayee
why the mouth became red colour ,,by the regular eating of leaf called ,,betel combining with areca?
jyotirmayee
all formula for calculate specific latent heat of any substance
hello
Nigar
Hi, your real Nigga...? Or this jock?
Arzoodan
real
Nigar
You from Pakistan or India?
Arzoodan
c'mon guys.. let's talk Physics.
Yoblaze
mass multiplied with latent heat of a substance
Yoblaze
Arzoodan
you both?
jyotirmayee
in which class?
jyotirmayee
physics is the only subject which underestimated chemistry ,,bio
jyotirmayee
how capacitor is made in inst?
Piyali
what is dipole moment
it is the product of electric charges and distance between the two charges
Shikhar
Arzoodan
mishra true thanks dia
Ssempala
product of separation of the poles, the rest shikhar got is right
brad is separation and distance ,are they different?
Ssempala
What is dielectric
its a type of medium. generally poor conductors. but their conductivity can be changed
vedanth
you just have to add impurities
vedanth
Thanks
Ssempala
grt
Ssempala
a material which behave as conductor
Shikhar
insulating material, energy level for electron transfer is very high e.g used to increase a magnetic field in a capacitor
What is the difference between specific heat capacity and heat capacity? Give the equations
presentation on power
relation between Celsius and Kelvin
0" degree Celsius=273kelvin
jyotirmayee
Newton's second laws is call with
what is mean by thermodynamics
it is study about temperature and it's equilibrium
thiru
Its the study of heat and its relation with others kind of energy
Antonio
state caulombs law clearly
show mathematically that an electron has the greater speed than the proton when they attract each other
show mathematically that an electron has the greater speed than the proton when they attract each other
srikanta
@ezra & srikanta; for electrons: a=ke^2/(mr^2) and for protons: a=kp^2/(mr^2)
Sikandar