20_562ln08

# 20_562ln08 - MIT OpenCourseWare http/ocw.mit.edu 5.62...

This preview shows pages 1–4. Sign up to view the full content.

MIT OpenCourseWare http://ocw.mit.edu 5.62 Physical Chemistry II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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

View Full Document
5.62 Lecture #20: Virial Equation of State Goal: Derive Virial Eqn. of State p = V A = kT ln V Q N , T N , T pressure ( 2 π mkT ) 3 N /2 Z N , V , T ) = ( 2 π mkT ) 3 N /2 V N exp N β N ⎞ ⎤ Q = N ! h 3 N ( N ! h 3 N 2 V ln Q = ln ( 2 π mkT ) 3 N /2 + N ln V + N N N ! h 3 N 2 V Plugging ln Q into equation for p … p = kT ( constants ) N lnV ( N 2 β /2V ) V + V + V N β N 2 NkT N 2 kT β = kT 0 + V 2V 2 = V 2V 2 Nk = nR, nN a = N N a n β ⎛ nRT pV N a β ⎛ RT RT + B 2 T V units Volume/mol . pV = nRT 2 V n pV = RT 2 V ( ) RT pV = RT + B 2 T V ( ) RT Virial Equation of State ( ) = 2 π N a 2nd VIRIAL COEFFICIENT B 2 T = N 2 a β 0 dr r 2 [e u(r)/kT 1] [The 1st VIRIAL COEFFICIENT, B 1 (T), is 1!]
Lecture #20, Page 2 As T → ∞ , B 2 ( T ) 0 because [ e u ( r ) kT 1 ] 0 At finite high T, B 2 ( T ) > 0 At low T, B 2 ( T ) < 0 low T — attractive forces dominate pressure is lower than ideal high T — repulsive forces dominate p is higher than ideal (pV = RT) Typical Values of B 2 (T) … in cm

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/27/2011 for the course CHEM 5.43 taught by Professor Timothyf.jamison during the Spring '07 term at MIT.

### Page1 / 8

20_562ln08 - MIT OpenCourseWare http/ocw.mit.edu 5.62...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online