{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# omg4 - Statistical Physics Example Sheet 4 David Tong March...

This preview shows pages 1–3. Sign up to view the full content.

Statistical Physics: Example Sheet 4 David Tong, March 2012 1i. By examining variations in E , F , H and G , derive the four diFerent Maxwell relations for the partial derivatives of S, p, T and V . ii. Obtain the partial derivative identity ∂S ∂T v v v v p = v v v v V + ∂V v v v v T v v v v p iii. Obtain the partial derivative identity ∂p v v v v V v v v v p v v v v T = 1 2. Consider a gas with a ±xed number of molecules. Two experimentally accessible quantities are C V , the heat capacity at ±xed volume and C p , the heat capacity at ±xed pressure, de±ned as C V = T v v v v V , C p = T v v v v p Using the results of the previous question, show that: i . C p C V = T v v v v p v v v v V = T v v v v 2 p v v v v T ii . ∂E v v v v T = T v v v v V p iii . v v v v T = T v v v v p p v v v v T iv . ∂C V v v v v T = T 2 p 2 v v v v V v . p v v v v T = T 2 V 2 v v v v p 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3. Consider a classical ideal gas with equation of state pV = Nk B T and constant heat capacity C V = B α for some α . Use the results above to show that C p = B ( α +1), and that the entropy is S = B log p V N P + B
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern