   Chapter 17, Problem 67AP

Chapter
Section
Textbook Problem

An x-ray tube used for cancer therapy operates at 4.0 MV, with a beam current of 25 mA striking the metal target. Nearly all the power in the beam is transferred to a stream of water flowing through holes drilled in the target. What rate of flow, in kilograms per second, is needed if the rise in temperature (ΔT) of the water is not to exceed 50.°C?

To determine
The rate of flow of water, in kilograms per second for 50°C rise in temperature.

Explanation

Given Info: X ray tube operates at 4.0MV . The X ray beam current is 25mA . It is assumed that all power of beam is transferred to flowing water. The rise in temperature during flow of water is 50°C .

Explanation:

Formula to calculate the power delivered by beam is,

Pbeam=IΔV

• Pbeam is the power delivered by the beam,
• I is the X ray beam current,
• ΔV is the operating voltage of X ray tube,

Substitute 25mA for I and 4.0MV for ΔV in the above equation to find Pbeam

Pbeam=(25mA)(10-3A1mA)(4.0MV)(106V1MV)=1.00×105W .(I)

The power delivered by beam to flowing water is 1.00×105W

Formula to calculate the power received by flowing water is,

Pwater=(mΔt)cΔT

• Pwater is the power received by flowing water from X ray beam,
• mΔt is the rate of flowing water, in kilogram per unit time,
• c is the specific heat capacity of water,
• ΔT is the change in temperature during water flow,

Substitute 4186JKg1(°C)1 for c and 50°C for ΔT in the above equation to find Pwater

Pwater=(mΔt)(4186JKg1(°C)1)(50°C)=2

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