Work done on system

Question

Suppose a gas of 2D atoms is trapped inside a square of area A.

What is the expression for the work done on the system as the area of the square changes?

Answer 1

The ideal gas law in 2D would be:

 

PA = nRT

 

Where A is the area.  The work done in compressing or expanding the gas is:

 

dW = -P dA

 

= -(nRT/A)*dA

 

Assuming an isothermal reaction, nRT = constant:

                _A2

W = -nRT ∫ dA/A   where A₁ is the starting area and A₂ in the ending area

               ^A1

W = -nRT (lnA₂ - lnA₁)

 

W = -nRT ln(A₂/A₁)