- #1

AmanWithoutAscarf

- 22

- 1

- Homework Statement
- According to the Eötvös rule, the surface tension is a linear function of the temperature, but I cannot find any theoretical proof of the function, except for the following excersise.

- Relevant Equations
- ##F=\sigma .L##

The translated version is:

I did research on the topic and the Eötvös rule, but most of the results are just qualitative explanations or experiment-based proofs of the temperature-dependent function of surface tension.

Can anyone give me some hints on how to prove that linear relation (using Carnot's theorem)? And the following questions, if possible, please.

1.Surface tension is temperature-dependent. Therefore, it is essential to specify the temperature when providing the surface tension value of an interface. Typically, surface tension decreases with increasing temperature and approaches zero at the critical temperature. This excersise will explore these concepts in detail.

a) Use Carnot's theorem to find the variation of surface tension ##σ## with temperature ##T##.

2.b) Calculate the temperature change of the liquid film during adiabatic expansion.

Inside a soap bubble of radius ##\displaystyle r_{0}## contains air (ideal gas) at temperature ##\displaystyle T_{0}## and pressure ##\displaystyle p_{0}##. The surface tension of the soap solution at this temperature is ##\displaystyle \sigma _{0}##. The specific heat of formation of a unit of soap film surface in an isothermal process is ##\displaystyle q_{0}##. Find the derivative of bubble radius with respect to temperature ##\displaystyle \frac{dr}{dT}## when ##\displaystyle T_{0}##. The outside pressure remains constant.

I did research on the topic and the Eötvös rule, but most of the results are just qualitative explanations or experiment-based proofs of the temperature-dependent function of surface tension.

Can anyone give me some hints on how to prove that linear relation (using Carnot's theorem)? And the following questions, if possible, please.