Solution Found!
Use a Maxwell relation from the previous problem 1 and the
Chapter 5, Problem 13P(choose chapter or problem)
Use a Maxwell relation from the previous problem 1 and the third law of thermodynamics to prove that the thermal expansion coefficient \(\beta \) (defined in Problem 2) must be zero at T = 0.
Questions & Answers
QUESTION:
Use a Maxwell relation from the previous problem 1 and the third law of thermodynamics to prove that the thermal expansion coefficient \(\beta \) (defined in Problem 2) must be zero at T = 0.
ANSWER:
Step 1 of 2
The thermal expansion coefficient \(\beta \) is defined as the fractional change in the volume per unit temperature change.
\(\beta = \dfrac{{\dfrac{{\Delta V}}{V}}}{{\Delta V}}\)
\(\beta = \dfrac{1}{V}{\left( {\dfrac{{\partial V}}{{\partial T}}} \right)_P}\)
Here, V is the volume, T is the temperature, and P is the system's pressure.