Relation between system enthelpy and surrounding entropy

[mooncrater]

Homework Statement

It is given in my book that:
ΔS_total=ΔS_system+ΔS_surrounding
Where S is entropy.
ΔS_surr=-ΔH/T
Therefore:
ΔS_total=ΔS_system+[-ΔH_system/T]

As we can see here that ΔS_surrounding=-ΔH_system/T
is applied here . But is this relation correct?

Homework Equations

ΔS=q_reversible/T
Where q_reversible is the heat input which is equal to ΔH(enthalpy) for constant P and T.

The Attempt at a Solution

What I think is that , instead of ΔH_system there should be ΔH_surroundings
Since the change in entropy of surroundings is taken. Am I correct here?

 

[Vatsal Sanjay]

You you consider system plus the surrounding to be an isolated system and apply conservation of energy, you will find the relation between ΔH_system and ΔH_surrounding
By the way you are correct here-

there should be ΔHsurroundings

And they have not used ΔH_system instead of ΔH_surrounding They have made use of the energy conservation equation I am talking about.

 

[mooncrater]

I think the relation you're talking about is
ΔH_system=-ΔH_surroundings
If energy is taken from the surroundings to the system.
Therefore when:
ΔS_system=ΔH_system/T will be equal to minus of ΔH_surroundings
/T
Am I correct here?

 

[Vatsal Sanjay]

Yes you're correct