X-Ray and Heat
Name: Rick M.
How many calories are generated at the plate of an x-ray
tube when 30,000 volts at 0.1 ma are applied?
Energy (joules) = voltage (volts) X current (amperes) = 30,000 X 0.1x10^-3
1calorie = 4.184 joules, so the energy in calories is 0.717 cal.
Power generated (or used) by a current I = q/t going through a voltage
drop V (= Ed) is given by P = IV. Here I = 0.0001 Amperes and V = 30,000
volts, so P = IV = 3 W.
Here I is the current in amperes, q is the charge in coulombs transferred
by the current in t seconds, E is the average electric field in
newtons/coulomb acting on the charge over a distance of d meters.
If you know that power is work done per unit time (P = W/t), that work is
given by force times distance (W = Fd), that the force exerted on a
charge of q coulombs by an electric field of E newtons per coulomb is
given by F = qE, and that E = V/d, this is easy to derive. Otherwise
ignore the next paragraph!
W = Fd = (qE)d; P = W/t = Fd/t = qEd/t = q(V/d)d/t = (q/t)V = IV
Best, Dick Plano...
Richard J. Plano
Actually, the question is incorrect. The number of calories produced will
depend on the length of time that the current flows through the tube. The
calorie is a unit of energy. If the tube is operating for twice as much
time, twice as much energy is produced. The milliamp,(1/1000 amperes),
however, is a rate: how many milliCoulombs of electric charge flow through
the tube per second. I will show you how to find the rate at which energy
is produced, often called "power".
The standard energy rate unit is the Watt: 1 Watt = 1 Joule per second. 1
calorie = 4.18 Joules. As for relating electric current and voltage to
energy, the product of the two is correct. (1 Volt)*(1 Ampere) = 1 Watt.
(30,000 Volts)*(0.1 x 10^-3 Amperes) = 3.0 Watts = 3.0 Joules/second
3.0 Joules/second *[1 calorie/4.18 Joules] = 0.72 cal/sec
In each second of current flow, 0.72 calories of electrical energy are
converted into x-ray radiation, heat, and possibly visible light. It may
not seem like a great deal of energy, but you must consider the source.
X-ray radiation interacts with individual cells. A cell can be destroyed
with just a little bit of energy, if that energy is in the right form.
Dr. Ken Mellendorf
Illinois Central College
(30,000 V) x (0.1 mA) = 3 Watts
This is equal to 3 Joules / Sec
This is 0.72 cals per sec (or 7.2 x 10-4 Cals / sec)
Hope this helps
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Update: June 2012