Change in Entropy for an isolated system

In summary, entropy is a measure of disorder in a system and is important in an isolated system because it helps us understand natural processes. The change in entropy for an isolated system can be calculated using the formula ΔS = Q/T and can never be negative due to the second law of thermodynamics. This change in entropy also affects the spontaneity of a process, as a positive change indicates spontaneity and a negative change indicates non-spontaneity. Furthermore, the change in entropy for an isolated system cannot be reversed due to the second law of thermodynamics.
  • #1
Pouyan
103
8
Homework Statement
Two systems, A and B, have the total constant heating capacities CA and CB as well as the initial temperatures TA and TB. They are put in contact with each other so that heat can be exchanged in a slow process without heat exchange with the surroundings. In the final state, both systems have assumed the same temperature. Determine the total entropy change in this process and show that it is positive.
Relevant Equations
dQ=TdS
dU=CdT
ΔU_A + ΔU_B = 0 (Is this because of isolated system am I right?)

ΔU_A = CA * (T_final - T_A )
ΔU_B=CB * (T_final-T_B)

And because of a very slow process : S=ln(T)
T_final= (CA T_A + CB T_B)/(CA + CB)

ΔS_final = CA*ln(T_f/TA) + ln(T_f/TB) * CB

My QUESTION is :

When we say No heat exchange with the surroundings or isolated system, do we mean ΔU=0 ?
 
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  • #2
Yes. Isolated means no work and no external heat exchange.
 

FAQ: Change in Entropy for an isolated system

What is entropy?

Entropy is a measure of the disorder or randomness in a system. It is a fundamental concept in thermodynamics and can be used to describe the direction of spontaneous processes.

How is entropy related to change in an isolated system?

In an isolated system, the total entropy remains constant. This means that any change in entropy in one part of the system must be offset by an equal and opposite change in another part of the system.

What causes a change in entropy for an isolated system?

A change in entropy for an isolated system can be caused by energy transfer, such as heat or work, or by a change in the number of microstates (possible arrangements of particles) in the system.

Can the change in entropy for an isolated system be negative?

No, the change in entropy for an isolated system can only be positive or zero. This is because the entropy of an isolated system cannot decrease, as this would violate the second law of thermodynamics.

How is entropy calculated for an isolated system?

The change in entropy for an isolated system can be calculated using the equation ΔS = Q/T, where ΔS is the change in entropy, Q is the heat added to the system, and T is the temperature in Kelvin. This equation is based on the relationship between entropy and energy in a system.

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