In general, = (, , , ) and other variables. Consider a system consisting of a spherical soap bubble. Since = () then we also note that = () where is the surface area of the bubble.

a) Since = (, , , ), expand in terms of and .

b) In this expansion, the coefficient for is the negative of the surface tension of the bubble, - . In a soap bubble, the surface tension can be considered as the force between the soap molecules that holds the bubble together. From the expansion you did in part (a), what is the thermodynamic definition of ?

c) What is the Maxwell relation associated with the differential expansion you found in part (a)?