# Change in Entropy of surroundings for irreversible process

## Homework Statement

I know that the equation ΔSsystem = Q/T is only valid for a reversible process but whenever i see problems involving a irreversible isothermal expansion of ideal gas, the ΔSsurroundings is taken as -Qirr/T. Why is that equation valid for surroundings, is it because the surroundings being a reservoir/sink, any heat exchange is done reversibly?

ΔSsystem = Q/T

Chestermiller
Mentor

## Homework Statement

I know that the equation ΔSsystem = Q/T is only valid for a reversible process but whenever i see problems involving a irreversible isothermal expansion of ideal gas, the ΔSsurroundings is taken as -Qirr/T. Why is that equation valid for surroundings, is it because the surroundings being a reservoir/sink, any heat exchange is done reversibly?

## Homework Equations

ΔSsystem = Q/T
This assumes that there are no significant temperature gradients present within the reservoir (so that the temperature of the entire reservoir is uniform) and that the reservoir temperature remains constant during the process. This can be approached in the real world by having the material in the reservoir consist of a mixture of liquid and solid at the melting point.

Chet