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$\bullet$$\bullet$ (a) A deuteron, $_{1}^{2} \mathrm{H},$ is the nucleus of a hydrogen isotope andconsists of one proton and one neutron. The plasma of deuterons in a nuclear fusion reactor must be heated to about 300 million K. What is the rms speed of the deuterons? Is this a significant fraction of the speed of light $\left(c=3.0 \times 10^{8} \mathrm{m} / \mathrm{s}\right) ?(\mathrm{b})$ What wouldthe temperature of the plasma be if the deuterons had an rms speed equal to 0.10$c ?$

a) $6.43 \times 10^{3}$b) $7.3 \times 10^{10}$

Physics 101 Mechanics

Chapter 15

Thermal Properties of Matter

Temperature and Heat

The First Law of Thermodynamics

The Second Law of Thermodynamics

University of Michigan - Ann Arbor

University of Washington

University of Sheffield

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this's checked her 15 problem over 22. We have a deodorant consists of Yes, a pizza nucleus of a hydrogen. Come. I said there were talking, but he has one proton and one neutral. So this is it, dude, Run. Right. And the plasma off dude around on a nuclear fusion reactor must be heated to about 300 1,000,000 into the power of a six. Calvin, Right. It has to be heated up to this temperature. And at this temperature, rest to calculate theorem. A speed of the ignorance. So b r A s. And then we're asked, Is this a sufficient fraction of the speed of light in part? A. So, in order to calculate the enormous well again, what? The deodorant since itself is a warning from talk. Let's remember that if one you do not correct me. So actually, we can calculate the mass of a dirt around here. Right? So the massive dude around is going to be recalled to the mass of a proton. Uh, what distance did Nicholas right eye and the mass of a neutron so massive a proton has bone find 673 times. Center for negative. 27 kilograms in the message when Trump is 1.675 Likely different, right? Tempter pro negative. 27 kilograms. So the total mass of of a dude around Nicholas is going to be 3.35 times 10 to go. Negative. 27 kilograms. Now we know the mass. We know the temperature. We should be able to calculate the r M. A steed cracked itself using the army. Speed equals 23 Katy over and right. So we know the mass, Uh, we know the balls one. Counselor, we know the temperature so we can can evacuate the armas speed. Um, let's do that three times. If you remember the value of the bolts one constant. It's 1.38 times center from negative. 23 jewels for molecule. Calvin. All right times we have the temperature 300 times. 10 to gore. Six kallman, 100,000,000 in denominator. We have less of the request. 3.35 times underground. Negative. 27 kilograms. Right. So the arm is speed. If from here is going to want a 270.93 times 10 to grove six meters per second. Compare this number to the speed of light that is three times 10 to farm eight years for second because in the second portion ofthe party, we were answering party, right? It says, Is this a significant fraction? Is this our Emma's speed? A significant fraction of the speed of light. Let's just going to meet the duration. Right. So the this arm s fee that we calculated groupie take first gracia 1.93 times something. There are six meters per second still out about three times from feet meters per second. It's gonna be cool to six point for three times center for negative three. So it's actually a very small fraction even though the temperature's pretty high right now and party were asked, what would the temperature of plasma be? So we're asked the temperature this time if deterrents had an a r m iss speed off one well, 10% of the speed of light pointing one times. See? So what this what this means is 10.1 kinds three times center for eight leaders for second. If this is our armas, are Emma's speed now, right? This is like three times something gross seven meters per second. Then what will be the temperature. Well, then, re actually using the same equation that we have raised three Katy over them. This time we're going to take the spare of fold sides, and we're going to solve it for temperature here. So the are best splinter equals 23 Katy over M. If we multiply both sides of this equation, I am over three k and over three K. Then we can help cancel our ends. We can cast like three K and then on the right hand side, I have the temperature equals to end the r m s squared over, um three k. So any twos this equation, then in order to calculate the temperature that corresponds to this Aramis speak, let's do it on the next page. So the temperature is going to be equal. Teo the Mass, which is 3.35 times center for negative 27 3 point here 35 times 10 to promote a 27 year old grams. Now our Aramis Speed square. So it is three point times three ten 10 cents of seven meters per second squared, divided by three times the walls one costume, 1.38 10 center from negative. 23 jewels. Her molecules, Helden, then the temperature. We're calculating it in terms of Calvin right, 7.3 times tentacle off 10 Calvin of even a is it? You see, high temperatures of the Army's is still a small fraction off the speed of light.

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