Amath105-5.pdf - W A = PdV W B = PdV V2 W A = PdV = PdV V1 A A W B = PdV = PdV V2 B Same for heat q A q A = q A = V1 Same for heat T2 T1 path has

# Amath105-5.pdf - W A = PdV W B = PdV V2 W A = PdV = PdV V1...

This preview shows page 1 - 6 out of 16 pages.

===21VVAAAPdVPdVWPdVWδSame for heat==21TTAAAAAqqqqδδδ===12VVBBBPdVPdVWPdVWδ==12TTBBBBBqqqqδδδpathhas direction Same for heatpathhas direction
III. Line integrals and III. Line integrals and multiple integralsmultiple integralsIntroduction• Line integral • Applied to Physical Chemistry I• Double integral• Jacobi determinant
IIIIII--5. Jacobi determinant5. Jacobi determinantJacobi determinant in one –dimensional case ( )( )()( )dydydxygdydydxyxfdxxf==Change from ( )yxxyx=:dyydydydxxdxxyx=⎯ →=21332For example:
Differential area element in Jacobi coordinateϕddxdyxx + dxyy+dyDifferential area element in polarcoordinate ϕρdρdρϕρddρϕρdddxdy=ρϕ(x, y)ϕρϕρsincos==yx
Jacobi determinant in two–dimensional case ()()()()()()()()()∫∫∫∫∫∫==ϕρϕρϕ

#### You've reached the end of your free preview.

Want to read all 16 pages?

• Spring '12
• logan

### 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