Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 25 - Optical Instruments - General Problems - Page 743: 79

Answer

The temperature rise per minute would be $4.8\times10^3 C^{\circ}$ without cooling water.

Work Step by Step

Assume that all of the electrical energy fed into the x-ray tube transforms into heat energy. $$P=IV=\frac{Q}{t}=\frac{mc\Delta T}{t}$$ We measure power in joules per second, so the kcal units in the specific heat should be converted to joules. Find the temperature rise per minute. $$\frac{\Delta T}{t}=\frac{IV}{mc}=\frac{(0.025A)(95000V)(60s/min)}{(0.065kg)(0.11kcal/(kg\cdot C^{\circ})(4186J/kcal))}$$ $$=4.8\times10^3 C^{\circ}/minute$$ Obviously, the cooling water is essential.
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