Question

Physics question on surface tension and thermodynamics?

We know, surface energy per unit area(E)=Mechanical energy(T) + heat(h)

How can we prove by thermodynamics that `h=-theta cdot (dT)/(d theta`

`theta` is absolute temperature.
`(dT)/(d theta)`=rate of change of surface tension with the increase of temperature.

Answer 1

See the explanation below

Explanation:

The mechanical work `W` needed to increase a surface area `A` is

`dW = γ dA`.

Where the surface tension is `=gamma`

Hence at constant temperature and pressure, surface tension

equals Gibbs free energy per surface area:

`gamma=((delG)/(delA))_(T,P,n)`

where `G` is Gibbs free energy and `A` is the area.

From this it is easy to understand why decreasing the surface area

of a mass of liquid is always spontaneous `(G < 0)`, provided it is

not coupled to any other energy changes. It follows that in order to

increase surface area, a certain amount of energy must be added.

Gibbs free energy is defined by the equation `G = H − TS`,

where `H` is enthalpy and `S` is entropy.

Based upon this and the fact that surface tension is Gibbs free

energy per unit area, it is possible to obtain the following

expression for entropy per unit area :

`((delgamma)/(delT))_(A,P)=-S_A`

Kelvin's equation for surfaces states that surface enthalpy or

surface energy depends both on surface tension and its derivative

with temperature at constant pressure by the relation

`H^A= gamma-T((delgamma)/(delT))_P`

This is the best I can do for this question!!