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Now let us take a look at the change in entropy of a Carnot engine and its heat reservoirs for one full cycle. The hot reservoir has a loss of entropy Δ S h = Q h / T h size 12{ΔS rSub { size 8{h} } = - Q rSub { size 8{h} } /T rSub { size 8{h} } } {} , because heat transfer occurs out of it (remember that when heat transfers out, then Q size 12{Q} {} has a negative sign). The cold reservoir has a gain of entropy Δ S c = Q c / T c size 12{ΔS rSub { size 8{c} } =Q rSub { size 8{c} } /T rSub { size 8{c} } } {} , because heat transfer occurs into it. (We assume the reservoirs are sufficiently large that their temperatures are constant.) So the total change in entropy is

Δ S tot = Δ S h + Δ S c . size 12{DS rSub { size 8{"tot"} } =DS rSub { size 8{h} } +DS rSub { size 8{c} } "." } {}

Thus, since we know that Q h / T h = Q c / T c size 12{Q rSub { size 8{h} } /T rSub { size 8{h} } =Q rSub { size 8{c} } /T rSub { size 8{c} } } {} for a Carnot engine,

Δ S tot =– Q h T h + Q c T c = 0 . size 12{DS rSub { size 8{"tot"} } "=-" { {Q rSub { size 8{h} } } over {T rSub { size 8{h} } } } + { {Q rSub { size 8{c} } } over {T rSub { size 8{c} } } } =0 "." } {}

This result, which has general validity, means that the total change in entropy for a system in any reversible process is zero.

The entropy of various parts of the system may change, but the total change is zero. Furthermore, the system does not affect the entropy of its surroundings, since heat transfer between them does not occur. Thus the reversible process changes neither the total entropy of the system nor the entropy of its surroundings. Sometimes this is stated as follows: Reversible processes do not affect the total entropy of the universe. Real processes are not reversible, though, and they do change total entropy. We can, however, use hypothetical reversible processes to determine the value of entropy in real, irreversible processes. The following example illustrates this point.

Entropy increases in an irreversible (real) process

Spontaneous heat transfer from hot to cold is an irreversible process. Calculate the total change in entropy if 4000 J of heat transfer occurs from a hot reservoir at T h = 600 K 327º C size 12{T rSub { size 8{h} } ="600"" K " left ("327"°C right )} {} to a cold reservoir at T c = 250 K 23º C size 12{T rSub { size 8{c} } ="250"" K " left (-"23" "." 0°C right )} {} , assuming there is no temperature change in either reservoir. (See [link] .)

Strategy

How can we calculate the change in entropy for an irreversible process when Δ S tot = Δ S h + Δ S c size 12{ΔS rSub { size 8{"tot"} } =ΔS rSub { size 8{h} } +ΔS rSub { size 8{c} } } {} is valid only for reversible processes? Remember that the total change in entropy of the hot and cold reservoirs will be the same whether a reversible or irreversible process is involved in heat transfer from hot to cold. So we can calculate the change in entropy of the hot reservoir for a hypothetical reversible process in which 4000 J of heat transfer occurs from it; then we do the same for a hypothetical reversible process in which 4000 J of heat transfer occurs to the cold reservoir. This produces the same changes in the hot and cold reservoirs that would occur if the heat transfer were allowed to occur irreversibly between them, and so it also produces the same changes in entropy.

Solution

We now calculate the two changes in entropy using Δ S tot = Δ S h + Δ S c size 12{DS rSub { size 8{"tot"} } =DS rSub { size 8{h} } +DS rSub { size 8{c} } } {} . First, for the heat transfer from the hot reservoir,

Δ S h = Q h T h = 4000 J 600 K = 6 . 67 J/K . size 12{DS rSub { size 8{h} } = { {-Q rSub { size 8{h} } } over {T rSub { size 8{h} } } } = { {-"4000"" J"} over {"600 K"} } "=-"6 "." "67"" J/K"} {}

And for the cold reservoir,

Δ S c = Q c T c = 4000 J 250 K = 16 . 0 J/K . size 12{DS rSub { size 8{c} } = { {-Q rSub { size 8{c} } } over {T rSub { size 8{c} } } } = { {"4000"" J"} over {"250 K"} } ="16" "." 0" J/K"} {}

Thus the total is

Δ S tot = Δ S h + Δ S c = ( 6 . 67 +16 . 0 ) J/K = 9.33 J/K. alignl { stack { size 12{DS rSub { size 8{"tot"} } =DS rSub { size 8{h} } +DS rSub { size 8{c} } } {} #" =" \( +- 6 "." "67 +16" "." 0 \) " J/K" {} # " =9" "." "33 J/K" "." {}} } {}

Discussion

There is an increase in entropy for the system of two heat reservoirs undergoing this irreversible heat transfer. We will see that this means there is a loss of ability to do work with this transferred energy. Entropy has increased, and energy has become unavailable to do work.

Questions & Answers

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Saud Reply
It is the ease with which electrical charges or heat can be transmitted through a material or a solution.
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how to find magnitude and direction
Arjune Reply
how to caclculate for speed
Arjune
derivation of ohms law
Kazeem Reply
derivation of resistance
Kazeem
R=v/I where R=resistor, v=voltage, I=current
Kazeem
magnitude
Arjune
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
Electric current is the flow of electrons
Kelly Reply
is there really flow of electrons exist?
babar
Yes It exists
Cffrrcvccgg
explain plz how electrons flow
babar
if electron flows from where first come and end the first one
babar
an electron will flow accross a conductor because or when it posseses kinectic energy
Cffrrcvccgg
electron can not flow jist trasmit electrical energy
ghulam
free electrons of conductor
ankita
electric means the flow heat current.
Serah Reply
electric means the flow of heat current in a circuit.
Serah
What is electric
Manasseh Reply
electric means?
ghulam
electric means the flow of heat current in a circuit.
Serah
a boy cycles continuously through a distance of 1.0km in 5minutes. calculate his average speed in ms-1(meter per second). how do I solve this
Jenny Reply
speed = distance/time be sure to convert the km to m and minutes to seconds check my utube video "mathwithmrv speed"
PhysicswithMrV
d=1.0km÷1000=0.001 t=5×60=300s s=d\t s=0.001/300=0.0000033m\s
Serah
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
why we cannot use DC instead of AC in a transformer
kusshaf Reply
becuse the d .c cannot travel for long distance trnsmission
ghulam
what is physics
Chiwetalu Reply
branch of science which deals with matter energy and their relationship between them
ghulam
Life science
the
what is heat and temperature
Kazeem Reply
how does sound affect temperature
Clement Reply
sound is directly proportional to the temperature.
juny
how to solve wave question
Wisdom Reply
I would like to know how I am not at all smart when it comes to math. please explain so I can understand. sincerly
Emma
Just know d relationship btw 1)wave length 2)frequency and velocity
Talhatu
First of all, you are smart and you will get it👍🏽... v = f × wavelength see my youtube channel: "mathwithmrv" if you want to know how to rearrange equations using the balance method
PhysicswithMrV
nice self promotion though xD
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thanks dear
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hi pls help me with this question A ball is projected vertically upwards from the top of a tower 60m high with a velocity of 30ms1.what is the maximum height above the ground level?how long does it take to reach the ground level?
mahmoud
please guys help, what is the difference between concave lens and convex lens
Vincent Reply
convex lens brings rays of light to a focus while concave diverges rays of light
Christian
for mmHg to kPa yes
Matthew
it depends on the size
Matthew Reply
please what is concave lens
Vincent
a lens which diverge the ray of light
rinzuala
concave diverges light
Matthew
thank you guys
Vincent
A diverging lens
Yusuf
What is isotope
Yusuf
each of two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties; in particular, a radioactive form of an element. "some elements have only one stable isotope
Karthi
what is wire wound resistors?
Naveedkhan Reply
Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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