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$\bullet$$\bullet$ At what temperature is the root-mean-square speed of nitrogen molecules equal to the root-mean-square speed of hydrogen molecules at $20.0^{\circ} \mathrm{C} ?$ (Hint: The periodic table in Appendix $C$ shows the molar mass (in $\mathrm{g} / \mathrm{mol} )$ of each elementunder the chemical symbol for that element. The molar mass of $\mathrm{H}_{2}$ is twice the molar mass of hydrogen atoms, and similarly for $\mathrm{N}_{2}.)$

3798 $\mathrm{C}^{\circ}$

Physics 101 Mechanics

Chapter 15

Thermal Properties of Matter

Temperature and Heat

The First Law of Thermodynamics

The Second Law of Thermodynamics

University of Washington

Simon Fraser University

University of Sheffield

Lectures

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$\bullet$ Oxygen $\left(\m…

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Determine the root-mean-sq…

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The root mean square speed…

00:51

The average speed (in mete…

06:38

For a gas of nitrogen mole…

02:08

The average speed of a nit…

06:16

Calculate the root mean sq…

01:41

Identify the gas whose roo…

03:34

Calculate the average spee…

06:10

The average speed of molec…

01:52

At what temperature (in $^…

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02:39

a) At what temperature do …

disrupter. 15. Problem number 26 were asked at what temperature? The Aramis feed of Lecter draw molecules equal to the Aramis speed of hydrogen molecule ahead 20 degrees Celsius. So overall for hydrogen, let's just Let's just first of all, remember the R. M s speed in terms of Moller masses. Sorry, mess. Speed is going to be equal to free our tea. Divided five The Moler, miss. Right. So in our problem, we want the R. M s speeds to be equal to each other for nitrogen and hydrogen molecules. Right? But they're mauler. Masses are different. So we know the Christ finding temperature of the hydrogen molecule. And we're trying to figure out what the temperature of the 19 molecules would be cool to if we want to have the same Artemus feed for both taps of gases. Right? So then the right hand side, the armas. If you're really the right hand side or let's say hydrogen, it's going to be three are temperature of the hydrogen was divided by the solar mass of the hydrogen. This is gonna correspond to enormous speed, and we want no problem. We want this to be evil, too. Thie are miss feed off the nitrogen. Falk. It's right. So then we're gonna put the temperature of the matter. Is your molecules here? And the modernise off the nitrogen? Then let's Well, as you can see, we don't need the gas constant or anything, because they're gonna cancel out. We have the same terms of inside three hours, but cancel out. Square worker's gonna cancel out. So what we have basically, is the temperature of the hydrogen molecule. The ratio of this is to the molar mass of a hydrogen, um equals to the temperature order hydrogen divided by more master. So if we multiply both sides by the morning mass on nitrogen, then these air going cancel out so that we can get to the final answer, right. Divided by elements of the hydrogen atom times did temperature off the hydrogen. Now let's see what's given to us in the problem where we don't let this isthe right. It's given to assist in any degree Celsius in the problem. Well, we're gonna convert it for Calvin milk. I've ever Let's just first calculate the mall arrests. Right. So, uh, let's say for ah, hydrogen. Well, we have two hydrogen is they're so per hydrogen. We have 1.8 grams promote. So that role, who have is 2.16 grams per family for the Moler mask off the nitrogen. We have two of them, right? Uh, I guess for me it's 14.7 said in a total, have 20 eat 0.14 grams her and again the temperature for hydrogen is given to us is 20 Reese else's. Let's convert that to children. So it's gonna be 2 93 count right now. Let's use the situation for everything in this equation stand. The temperature for the nitrogen is going to be equal to 28.14 friends from all times. 2 93 Kallman divided by 2.16 friends for all right. It's a good cast locked. So the temperature of the nitrogen, huh has to be 4,071. Almost 4,071 Calgon that more or less equals 23 800 Cell sees

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