# Entropy of system and surroundings

• Titan97
In summary, there are various processes and factors that affect entropy change, such as reversible adiabatic and isothermal processes, phase changes, and the handling of the surroundings during a process. The change in entropy of the system and surroundings may not always be equal and can be influenced by the methods used to bring about the change. To ensure that the surroundings is handled reversibly during a process, a special tool kit consisting of tiny weights and constant temperature reservoirs can be used.

#### Titan97

Gold Member
I have some doubts on entropy change of certain simple process. Can you check if these statements are correct? This is what I know:

For a reversible adiabatic process, $$\Delta Q=0$$. $$\Delta S_{system}=\frac{\Delta Q}{T}=0$$.
Since the system does not alter the surroundings, ##\Delta S_{Surr}=0##.

For a reversible isothermal process, $$\Delta S_{system}=nR\ln{\frac{V_2}{V_1}}$$
How can I compute ##\Delta S_{Surr}##?.

For any phase change, since temperature and pressure is constant,
$$H=U+pV$$
$$dU=dQ-pdV$$
$$dH-d(pV)=dQ-pdV$$
$$dH=dQ+VdP=dQ$$
since P is constant.
Hence, $$dS_{sys}=\frac{dH}{T}$$
How can I compute ##\Delta S_{Surr}##?.​

For example, if an ice melts, ice is the 'system' and the medium where its kept is the 'surroundings'
The statements in red are questions. Those in blue means 'I am not sure if its correct'. (I might have written meaningless/incorrect/stupid statements. I just want to be clear with entropy before writing my exam.)

But Q_surroundings may not always be equal to -Q_system.

Should I use ΔS_(surr) + ΔS_(sys) ≥ 0?

But that won't give the exact value.

If a closed system is subjected to a reversible process, there is no guarantee that the surroundings is also handled reversibly during the process. For example, if you bring about an adiabatic reversible compression of a gas within a cylinder by hand (say by very gradually subjecting the gas to increasing pressure using a piston attached to a rod being pushed by your hand), the change in entropy of your body (which basically constitutes the surroundings) certainly will be positive. On the other hand, if the same change is brought about by sliding tiny weights onto the piston at different elevations, the change in entropy of the surroundings will be zero.

Moran et al, Fundamentals of Engineering Thermodynamics define "Internally Reversible Processes." These are processes for which the system experiences a reversible change without specifying whether the surroundings are handled reversibly or irreversibly.

If you want to make sure that the surroundings is always handled reversibly during all changes you consider, I have a special tool kit that one can use. It consists of two kinds of items: (a) a set of tiny weights that can be applied to change the pressure gradually and (b) an infinite array of constant temperature reservoirs at different temperatures, so that the system can be contacted with a sequence of reservoirs at gradually increasing- or gradually decreasing temperatures. This should do the trick.

Chet

## What is entropy and why is it important in science?

Entropy is a measure of the disorder or randomness in a system. In science, it is important because it helps us understand the direction in which a system will naturally evolve and the efficiency of energy transformations.

## How is entropy related to the laws of thermodynamics?

Entropy is closely related to the second law of thermodynamics, which states that the total entropy of a closed system and its surroundings will always increase over time. This means that in any natural process, the total entropy of the universe will always increase.

## What factors affect the entropy of a system and its surroundings?

The entropy of a system and its surroundings can be affected by temperature, pressure, and the number of particles present. Generally, increasing the temperature or volume of a system will increase its entropy, while decreasing the temperature or volume will decrease its entropy.

## What is the difference between entropy of a system and entropy of its surroundings?

The entropy of a system refers to the disorder or randomness within the system itself, while the entropy of its surroundings refers to the disorder or randomness in the environment surrounding the system. Both are important in determining the overall change in entropy during a process.

## Can entropy be reversed or decreased?

According to the second law of thermodynamics, the total entropy of a closed system and its surroundings will always increase over time. While it is possible to decrease the entropy of a system, it would require an input of energy and would result in an even greater increase in entropy in the surroundings.