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Integrated ConceptsSingly charged gas ions are accelerated from rest through a voltage of 13.0 V. At what temperature will the average kinetic energy of gas molecules be the same as that given these ions?
$T=1.00 \times 10^{5} \mathrm{K}$
Physics 102 Electricity and Magnetism
Chapter 19
Electric Potential and Electric Field
Electric Charge and Electric Field
Gauss's Law
Electric Potential
University of Michigan - Ann Arbor
University of Washington
Hope College
University of Sheffield
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to solve this question, we have to understand how much energy is there in electric field. And then it equated to the kinetic energy off gas molecules. No energy, an electric field. Let's say E is equal to charge times two potential. We are given the charge askew, but the potential is given That's 13 vote. See his cute times 13 on DDE were also given that energy due to kinetic energy. Kinetic motion off a guest is 3/2 okay, which is Bozeman Constant. So let me ride book being the as a superstar subscript. And then let's quit them. So we have to find the temperature, just tea and temperature you will find in Kelvin Kim. Times V. So the temperature now is equal to Q times. The charge. It's said that it's single charged. It means it has a child off 1.6 times. 10 power Negative 19 which is one Elektronik charge Times the voltage is 13. Divided by three. Huh, Bozeman Constant, which is 1.38 times 10 power Negative. 23. So if you do this calculation, you will get the value off the order of 10 power for from the 10 Power negative 19 and a negative 23. And let me do the calculation on my calculator for at Their Numbers, which is 1.6 times 13 divided by 1.5, divided by 1.38 which is 10. So the answer here is 10 power five Kelvin. See, in this case, to solve this question, I have used the concept off electric energy on the kinetic energy for gas and then equated them in the third step here. So this is first step, second step, third step, So if you can do these steps, solution is quite easy.
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