Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication.The thermodynamic concept was referred to by Scottish scientist and engineer Macquorn Rankine in 1850 with the names thermodynamic function and heat-potential. In 1865, German physicist Rudolph Clausius, one of the leading founders of the field of thermodynamics, defined it as the quotient of an infinitesimal amount of heat to the instantaneous temperature. He initially described it as transformation-content, in German Verwandlungsinhalt, and later coined the term entropy from a Greek word for transformation. Referring to microscopic constitution and structure, in 1862, Clausius interpreted the concept as meaning disgregation.A consequence of entropy is that certain processes are irreversible or impossible, aside from the requirement of not violating the conservation of energy, the latter being expressed in the first law of thermodynamics. Entropy is central to the second law of thermodynamics, which states that the entropy of isolated systems left to spontaneous evolution cannot decrease with time, as they always arrive at a state of thermodynamic equilibrium, where the entropy is highest.
Austrian physicist Ludwig Boltzmann explained entropy as the measure of the number of possible microscopic arrangements or states of individual atoms and molecules of a system that comply with the macroscopic condition of the system. He thereby introduced the concept of statistical disorder and probability distributions into a new field of thermodynamics, called statistical mechanics, and found the link between the microscopic interactions, which fluctuate about an average configuration, to the macroscopically observable behavior, in form of a simple logarithmic law, with a proportionality constant, the Boltzmann constant, that has become one of the defining universal constants for the modern International System of Units (SI).
In 1948, Bell Labs scientist Claude Shannon developed similar statistical concepts of measuring microscopic uncertainty and multiplicity to the problem of random losses of information in telecommunication signals. Upon John von Neumann's suggestion, Shannon named this entity of missing information in analogous manner to its use in statistical mechanics as entropy, and gave birth to the field of information theory. This description has been proposed as a universal definition of the concept of entropy.
Homework Statement
Premium gasoline produces 1.23×108 J of heat per gallon when it is burned at a temperature of approximately 400ºC (although the amount can vary with the fuel mixture). If the car's engine is 25.0% efficient, three-fourths of that heat is expelled into the air, typically at...
I have seen in a number of thermodynamics lectures that the entropy change of a system as it falls approximately isothermally from some height h to the ground is: ΔS = mgh/T
(The proof basically has you conceive of a reversible process between the same two states where some upwards force acts...
Homework Statement
S(E,V) = kln(\Gamma(E) )\\
S(E,V) = kln(\omega(E) )\\
S(E,V) = kln(\Sigma(E) )\\
S entropy, k Boltzmann's constant. Prove these 3 are equivalent up to an additive constant.
Homework Equations
\Gamma(E) = \int_{E<H<E+\Delta}^{'}dpdq\\...
Combining first and second law of thermodynamics we can get the following equation
TdS=dU-PextdV
First question: Is this equation available for irreversible process that dS≠dQ/T?
Second question:If the system temperature Tsys is smaller than the surrounding temperature Tsur, which...
The usual "proof" entropy is a state property is like that:
"Consider a system which undergoes a reversible process from state 1 to state 2 along path A, and let cycle be completed along path B, which is also reversible. Since the cycle is reversible we can write:
∫1-2 δQ / T + ∫2-1 δQ / T...
Hello guys,
I was watching video about physical basis for arrow of time..
..as well as several other videos and articles about physics of time. I am puzzled with this picture here (seen in 35:07 in video above)...
I'm having trouble getting my head around entropy. In an isolated system, entropy can only remain the same or increase. Is this the same for a thermodynamics cycle? What I mean is, if I drew a cycle on a PV diagram, would the entropy keep increasing? I can't see how that would work, that would...
When:
- Vacuum had an absolute mass, relatively limiting expension of all universal matter
- Newton's second law could be overridden or negated
- [Anything else I couldn't think of]
I am presented a review of data which gives:
vapour pressures of a liquid have been measured and fit to the following equation:
Log10 (mmHg) = -3571/T + 8.999
The melting point has been determined to be 392.7 K.
A Cp value given for the liquid is 250 J/mol K
and the ΔSvap is 117 J/mol K...
Homework Statement
Homework Equations
The Attempt at a Solution
I don't know what is the difference between the change in entropy of the gas vs the thermal reservoir??
1) What is the reason why dH!=0 for an adiabatic(q=0) reversible process?
The mathematical argument is irrefutable and it is clear that it has to do with the process not being isobaric:
ΔH=ΔU+PΔV+VΔP , ΔU=work=−PΔV
Therefore, ΔH=VΔP and this is not 0.
However, I do not understand it...
Hello. I was reading Hyperphysics website and could not get one particular part. I am providing a picture of the equation I am having trouble with: http://i.snag.gy/W3CC3.jpg
The particular part that puzzles me is the relation around the third equation sign. From the formula there one can think...
Homework Statement
Vapour pressures of a liquid have been measured and fit to the following equation:
Log10 P (mmHg) = -3571/T + 8.999
The melting point has been determined to be 392.7 K.
A Cp value given for the liquid is 250 J/mol K
and the ΔSvap is 117.20 J/mol K
Homework Equations...
We Now From Information Theory That Entropy Of Functions Of A Random Variable X Is Less Than Or Equal To The Entropy Of X.
Does It Break The Second Law Of Thermodynamic?
Homework Statement
vapour pressures of a liquid have been measured and fit to the following equation:
Log10 (mmHg) = -3571/T + 6.124
The melting point has been determined to be 392.7 K.
A Cp value given for the liquid is 250 J/mol K
and theΔSvap is 117 J/mol K
Homework Equations...
Homework Statement
The vapour pressures of a liquid have been measured and fit to the following equation:
Log10 (mmHg) = -3571/T + 6.124
The melting point has been determined to be 392.7 K.
Calculate the standard entropy of the liquid at the melting point.
Homework Equations...
No heat exchange is facilitated during an adiabatic process. Change is heat is zero.
How does this relates to the entropy being zero?
∫dQ/T?
But this could really just mean that the integral is of any constant.
okay so I suck at La-Tex so I'm not going to put the actual equation, but it's not important for my question.
In the equation the entropy is dependent on the natural log with mass in the numerator of the argument. Why is mass involved when talking about entropy at all?
I mean I think of...
I have a short question which I have been discussing with a fellow student and a professor. The question (which is not a homework question!), is as follows:
If you shift all the energies E_i \to E_i + E_0 (thus also shifting the mean energy U \to U + E_0), does the entropy of the system remain...
Calculate the change in entropy of the Universe as a result of the following
operations:
(a) A copper block of mass 0.4kg and thermal capacity 150JK-1 at 100◦C is
placed in a lake at 10◦C.
dS=dQ/T dQ=mCdT
Tried simply combining these equations and integrating to find change of entropy of...
Hello, I am looking for some clarity on the second law of thermodynamics. I am an amateur physics student and only just beginning and so my understanding is currently very basic!
I have watched Brian Cox's Wonders of the Universe, where he talks about the second law of thermodynamics being...
Homework Statement
Suppose we put N atoms of argon into a container of volume V at temperature T. Of these N atoms, Nad stick to the surface, while the remainder Ngas = N - Nad form an ideal gas inside the container.
Assume that the atoms on the surface are not able to move and have an...
There is one paragraph that says:
"
Our starting assumption is directly motivated by Bekenstein's original thought experiment
from which he obtained is famous entropy formula. He considered a particle with
mass m attached to a ctitious "string" that is lowered towards a black hole. Just...
Hello
Homework Statement
From the expression of the partition function of a fermi dirac ideal gas
ln(Z)=αN + ∑ ln(1+exp(-α-βEr))
show that
S= k ∑ [ <nr>ln(<nr>)+(1-<nr>)ln(1-<nr>)
Homework Equations
S=k( lnZ+β<E>)
<nr>=-1/β ∂ln(Z)/∂Er
<E>=-∂ln(Z)/∂β
The Attempt at a Solution
I...
1.0 mol of N2O4 placed in a constant pressure vessel at P = 1bar and T = 298 K. The system is allowed to slowly (reversibly) come to equilibrium. Given gibbs energy of formation, enthalpy of formation and entropy (the values are below) calculate the entropy change to the surroundings.
N2O4...
Homework Statement
Four moles of an ideal gas expands at constant temperature until its pressure is reduced to half of its initial value. What is the change in entropy of the gas?
Homework Equations
ΔS=Q/T (For constant T) pinitial=p pfinal=.5p
Q=W
W=pdv
nrTln(vf/vi)
The Attempt...
Any state analytic in energy (which includes most physical states since they have bounded energy) contains non-local correlations described by the Reeh-Schlieder theorem in AQFT. It is further shown that decreasing the distance between wedges will increase the entanglement as measured by a...
Homework Statement
a)A stone at 400K with heat capacity ##c_p## is placed in a very large lake at 300K. The stone cools rapidly to 300K. Calculate the entropy change, due to this process, of the stone and lake.
b)An insulated cool-box of a Carnot refrigerator at temperature T loses heat...
Homework Statement
For a box containing 1m^{3} of nitrogen at S.T.P., estimate the number of microstates which make up the equilibrium macrostate.
Homework Equations
S = Nk_{b}(ln\frac{V}{N} + \frac{5}{2} + \frac{3}{2}ln\frac{2πmk_{b}T}{h^{2}})
where the entropy of a volume, V ...
Homework Statement
5. The nuclei of atoms in a certain crystalline solid have spin one. Each nucleus can be in anyone of three quantum states labeled by the quantum number m, where m = −1,0,1. This quant number measures the projection of the nuclear spin along a crystal axis of the solid. Due...
Please see attached picture.
I need verification of my answers. I unfortunately found these problems on an old book with no answer. I would really appreciate it.
(a) Ok. For this one, I am really not sure. PLEASE help.
I get a very complicated formula.
(1+x)(x^4)/(1-x)^2=Kp.
Now, this...
I know how to get Von Neumann entropy from a density matrix. I want to get a real number from measurements that give real numbers as outcomes. (there are complex numbers in a density matrix).
So suppose Charlie sends 1000 pairs of particles in the same state to Bob and Alice. They agree to...
I was following along in my Thermodynamic textbook and began playing with some definitions. In the following formulation, I somehow managed to prove (obviously incorrectly) that dq = TdS for even irreversible processes. I was hoping someone could point out where in the proof I'm going wrong...
Homework Statement
A 3.5 kg block of cobber at 100 degrees celsius (373 K) is put in 0.8 kg water at 0 degrees celsius (273 K).
The equilibrium temperature is 30 degrees celsius (303 K).
Calculate the change of entropy for the system of cobber and water.
Homework Equations
ΔS=\frac{Q}{T}...
Ok so entropy cannot be destroyed, right? So let's say you have a reaction that decreases entropy (s<0) but it also is exothermic (h<0) and that overpowers the entropy decrease so it is spontaneous (ie h-ts=g<0). If that happens, where does the entropy go?
In the Gibbs free energy equation, does the standard change in entropy equal q(sys)/T(system)?
Or in math terms:
T(surr) * q(sys)/T(sys) = T(surr) * dS(standard)
Thus
dS(standard) = q(sys)/T(sys)
(surr) = surroundings
(sys) = systems
(standard) = at standard conditions
Homework Statement
Is boiling of egg accompanied by an increase in entropy?
The Attempt at a Solution
I guess entropy decreases because as the egg boils, the stuff inside it gets hardened and changes into a solid mass. So the disorderliness decreases and the entropy should decrease. But...
Homework Statement
The temperature at the surface of the Sun is approximately
5 700 K, and the temperature at the surface of the
Earth is approximately 290 K. What entropy change
occurs when 1 000 J of energy is transferred by radiation
from the Sun to the Earth?
Homework Equations...
Homework Statement
As a model of a paramagnet, consider a system of N fixed particles with spin 1/2 in a magnetic fiels H along z axis. Each particle has an energy e=μH (spin up) or e=-μH
Using S=kln(Ω), show that
S=k [ (N-E/e)/2 ln( 2N/(N-E/e) ) + (N+E/e)/2 ln( 2N/(N+E/e) ) ]...
"Dumping" Entropy
Hello everyone,
I am reading Daniel Schroeder's Thermal Physics book. One phrase he uses that I find particular confusing is that a system has to "dump" entropy. As one example, in chapter 5 he briefly discusses how a fuel cell functions, stating, "In the process of...
From Statsitical And Thermal Physics (Reif. international edition 1985)
160 page. (5.4.4)
S(T,V;√) = √[∫{cv(T`)/T`}dT` + Rln(V) - Rln(√) + constant]
(integral is from T0 to T , cv is specific heat)
This is a entropy of system for temperature 'T' , Volume 'V' , Moles '√' <--...
Hi..
Consider a rod which is insulated on its lateral surface, now this rod is brought in contact with a source at temperature T1 and sink at temperature T2 now a temperature gradient sets up in the rod after steady state is reached temperature at some distance X from the source end is given as...
hi to everybody out there,
entropy as i know of now is associated with heat which is basically energy in transit(for a rev. process it is indicative of unavailable part of energy) having said that what is meant by entropy change for a system as heat flows into or out of it(for instance consider...
Homework Statement
Show using Boltzmann's principle (S=k.lnW), show that with respect to changes in V and T:
dS=k.N.\frac{dV}V{}+\frac{C.dT}V{T}
Where W=T^{\frac{C}k{}}V^{N}The Attempt at a Solution
S=k.lnT^{\frac{C}k{}}V^{N}=k.lnT^{\frac{C}k{}}+klnV^{N}
S=C.lnT+N.lnV
Now I know that the...
Hello,
I'm studying for my exam for tomorrow and we solved an exercise in class , but a question was not answered and I don't know how to solve it.
Homework Statement
1 Kg of water is heated at 0 degree C is brought into contact with a large heat reservoir at 100 degrees C. When the water...
One mole of an ideal monatomic gas initially at 298 k expands from 1.0 L to 10.0 L. Assume the expansion is irreversible, adiabatic, and no work is done. Calculate delta S of the gas and delta S of the surroundings.
I know that delta dS = dq/T but q = 0 in adiabatic processes right? So does dS...
Hello,
Do living beings use food to decrease the entropy of his body?
If so, could anyone explain the process of how we do it? (or at least name a couple of keywords that I can search)
Thank you very much.