# Entropy of system and surroundings

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.)

Homework Helper
Gold Member
But Q_surroundings may not always be equal to -Q_system.

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

But that wont give the exact value.

Mentor
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