problem17_p121

# University Physics with Modern Physics with Mastering Physics (11th Edition)

• Homework Help
• PresidentHackerCaribou10582
• 2

This preview shows pages 1–2. Sign up to view the full content.

17.121: For a spherical or cylindrical surface, the area (17.21) Eq. in A is not constant, and the material must be considered to consist of shells with thickness dr and a temperature difference between the inside and outside of the shell . dT The heat current will be a constant, and must be found by integrating a differential equation. a)Equation (17.21) becomes . 4 or ) 4 ( 2 2 dT k πr dr H dr dT πr k H = = Integrating both sides between the appropriate limits, ). ( 1 1 4 1 2 T T k b a π H - = - In this case the “appropriate limits” have been chosen so that if the inner temperature 2 T is at the higher temperature 1 T , the heat flows outward; that is, . 0 < dr dT Solving for the heat current, . ) ( 4 1 2 a b T T πab k H - - = b) Of the many ways to find the temperature, the one presented here avoids some intermediate calculations and avoids (or rather sidesteps) the sign ambiguity mentioned above. From the model of heat conduction used, the rate of changed of temperature with radius is of the form B r B dr dT with , 2 = a constant. Integrating from

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

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