By Third Law of thermodynamics;
s = k ln(p)
where;
s = entropy
k=Boltzmann constant
p= Probability of finding a molecule at a particular point
When temperature rises, anyhow, Internal energy and hence the kinetic energy (k.e)increase as well for the ideal substance. Increased k.e calls for more randomness of particles which would certainly change the probability and hence the entropy.
This belies the common processes that we encounter in many power cycles. Where does it go wrong?
Reversible adiabatic compression of a perfect gas will be an isentropic process occurs with increasing temperature. By the first law the increment of internal energy, which is equal to Cv. (T2-T1) is equal to the work applied to compress adiabatically and reversibly the ideal gas, as applied W is positive, must be T2> T1.
You can not assume that increase in temperature for an ideal system increases the number of states and thus randomness. As long as number of energy states remains the same, entropy will not alter even if you use this statistical expression of Boltmann to calculate entropy.
Mr. Jindal sir, can you please elaborate the concept of number of states?
I think you are trying to connect the thermodynamic and classical mechanics interpretation of entropy....
Dear Saransh,
do not write s = k ln p. The probability of finding a molecule at some point in space is zero. With continuous systems, you can only use probability densities.
The law should be S = k ln W, where W is the number of arrangements of your system. This is the equation on Boltzmann's gravestone.
Concerning your question: You should distinguish between internal and external entropy (changes). External changes usually refer to heat exchanged with the
environment, dS_ex = dq / T. If you thermally isolate your system, dS_ex = 0 by definition, even if the system temperature changes. Adiabatic compression is such a process, as explained by Vicente. Internal entropy is related to molecular disorder, tries to become maximal in insulated systems, and can be calculated with Boltzmann's equation.
Entropy: A concept that is not a physical quantity
https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity
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