# Entropy change for non-thermally-isolated system

• wumple
In summary, Reif states that if the external parameters of a thermally isolated system are changed quasi-statically, the entropy change will be zero. This is because there is no heat transfer (Q = 0) and the entropy relation dS = dq/T does not include work. However, in a non-thermally isolated system, the entropy change of the universe is still zero due to the equal and opposite entropy changes in the system and surroundings. In the example of isothermal expansion, the entropy gain of the gas is equal to the entropy lost by the surroundings, resulting in a net entropy change of zero for the universe.
wumple

## Homework Statement

This isn't an actual problem, it's just a question based on my reading. Reif says "If the external parameters of a thermally isolated system are changed quasi-statically by any amount, ΔS = 0."

I don't understand why it has to be thermally isolated. Looking at the entropy relation

$$dS = dq/T$$

There isn't any work in there, and the derivation didn't set work = 0. So if a system undergoes a reversible process and dQ is non-zero, it seems that work also has no effect on the entropy change?

wumple said:

## Homework Statement

This isn't an actual problem, it's just a question based on my reading. Reif says "If the external parameters of a thermally isolated system are changed quasi-statically by any amount, ΔS = 0."

I don't understand why it has to be thermally isolated. Looking at the entropy relation

$$dS = dq/T$$

There isn't any work in there, and the derivation didn't set work = 0. So if a system undergoes a reversible process and dQ is non-zero, it seems that work also has no effect on the entropy change?

We have the system and we have the surroundings. The two together form the "universe".

If the system is thermally isolated from the surroundings, Q = 0 by definition and so is ΔS = Q/T, no matter how T may change during the process. So ΔS = 0 for the system, surroundings and universe.

If on the other hand the system is not thermally isolated, then heat can, for example, get into the system from the surroundings. If the process is reversible though, entropy gained by the system = entropy lost by the surroundings. Entropy change of the universe = 0.

Example: isothermal expansion of an ideal gas. We supply heat to the gas, keeping T constant, allowing it to expand from V1 to V2 and p1 to p2. ΔU = 0 so 1st law reads Q = W = ∫pdV = nRT∫dp/p from p1 to p2 = nRT*ln(p2/p1). So the gas increases entropy by Q/T. This amount obviously is lost by the surroundings. The universe entropy change is Q/T - Q/T = 0.

## 1. What is entropy change for a non-thermally-isolated system?

The entropy change for a non-thermally-isolated system refers to the change in the amount of disorder or randomness of a system that is not completely isolated from its surroundings. This means that the system can exchange energy with its surroundings, resulting in changes in its entropy.

## 2. How is entropy change calculated for a non-thermally-isolated system?

The entropy change for a non-thermally-isolated system can be calculated using the equation ΔS = Q/T, where ΔS is the change in entropy, Q is the heat transferred, and T is the temperature at which the heat transfer occurs.

## 3. What factors can affect the entropy change for a non-thermally-isolated system?

The entropy change for a non-thermally-isolated system can be affected by several factors, including the temperature difference between the system and its surroundings, the amount of heat transferred, and the nature of the system itself.

## 4. Why is the concept of entropy change important for non-thermally-isolated systems?

The concept of entropy change is important for non-thermally-isolated systems because it helps us understand how energy is transferred and how disorder or randomness is affected in these systems. This can have implications in various fields such as thermodynamics, chemistry, and biology.

## 5. Can entropy change be negative for a non-thermally-isolated system?

Yes, entropy change can be negative for a non-thermally-isolated system. This means that the system has become more ordered or less random after a heat transfer. However, in most cases, entropy change tends to be positive as systems tend to become more disordered over time.

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