To solve the problem it is necessary to apply the concepts related to Helmholtz free energy. By definition in a thermodynamic system the Helmholtz energy is defined as
[tex]\Delta F = \Delta U - T\Delta S[/tex]
Where,
[tex]\Delta U[/tex] is the internal energy equivalent to
[tex]\Delta U = C \Delta T[/tex]
And [tex]\Delta S[/tex] means the change in entropy represented as
[tex]\Delta S = C ln \frac{T_2}{T_1}[/tex]
Note: C means heat capacity.
Replacing in the general equation we have to
[tex]\Delta F = C \Delta T - T C ln \frac{T_2}{T_1}[/tex]
The work done of a thermodynamic system is related by Helmholtz free energy as,
[tex]W = - \Delta F[/tex]
[tex]W = -(C \Delta T - T C ln \frac{T_2}{T_1})[/tex]
[tex]W = T C ln \frac{\T_2}{T_1}-C \Delta T[/tex]
Replacing with our values we have,
[tex]W = (293.15)(1.2)ln(\frac{293.15}{273.15})-(1.2)(20)[/tex]
[tex]W = 0.858 J[/tex]
Therefore the maximum work that can be accomplished is 0.858J
