5

What is the temperature (in K) of a sample of helium with an root- mean-square velocity of 442.0 m/s? The universal gas constant; R-8.3145 Jlmol K...

Question

What is the temperature (in K) of a sample of helium with an root- mean-square velocity of 442.0 m/s? The universal gas constant; R-8.3145 Jlmol K

What is the temperature (in K) of a sample of helium with an root- mean-square velocity of 442.0 m/s? The universal gas constant; R-8.3145 Jlmol K



Answers

At what temperature will the particles in a sample of helium gas have an $\mathrm{rms}$ speed of $1.0 \mathrm{~km} / \mathrm{s}$ ?

Hi there. So for this problem, we need to determine at what in parador the atoms of helium gas have the same R. M. S. Speed or as the molecules of hydrogen gas at a temperature tour of the temperature or is equal to 26 C degrees. No, we know that. The root mean square A speed. Mhm. And we know that that is proportional to the square of the temperature. Soar over the mass. Now, we must remember that the the atoms of alien gas have the double of the mass of the molecules of hydrogen gas. So with that set, if we take um if we have, for example, the R. M. S. Speed for alien, we can uh right. That that is two times the mass over the temperature for we're gonna call this for alien. Meanwhile, for the R. M. S. Speed of hydrogen, we will have that that is the square root, Well, it's proportional to the square root of the temperature or of hydrogen over the mass of hydrogen. So, if we divide this value by this, if we take the if we take the ratio between those two, we will have that these over to em it's equal and this and over this barry tour of hydrogen. Um So as you can see, we can simplify this further, remember that since they need to have the same and root mean square speed, this is going to be equal to one. So, and here what we can do is to elevate this to the square both sides to the square because the square of one is just one. So we will have that, that is the temperature of alien over two times the mass of this because that's the mass of that. And this over the temperature or of hydrogen over the mask of hydrogen. And in here, as you can see this goes away with this and we will find that of course this is equal to one. But in here we will have them that the temperature of alien over the temperature of hydrogen Is equal to two. So we will find that the temperature of alien is equal to two times the temperature of hydrogen. And we have the temperature of hydrogen. Is this one that is given in here. So the first thing that we need to transform this well we can leave it like that but we can transform this into Into Calvin. So we need to add to that value 273 Calvin. So from that we obtain about you of 299 Calvin. So we substitute that value in here. So we will obtain that the temperature of heli in such that he has the same velocity of RMS velocity of the molecules of hydrogen is 590 eight killed in that we can also transform into Celsius degrees by strapped into that about you 273. So from this we obtain about you in Celsius degrees of 325 Celsius degrees. So this is a solution for this problem. Thank you.

Let's first discuss why we even calculate the room. The root mean square. My apologies. We calculate the root mean square to find the speed at which particles air randomly moving in gashes face. And this is this will be the reasoning Why we even do this problem for part A. We know that our temperature is 500 Kelvin, and we know that the muller weight of helium is 4 g per mole. We can really easily convert that in 2 kg to say that the mother weight of helium is four times 10 to the negative third kilograms Promote. Now if we want to find the root mean square which all to know what the letter C of helium. It's equivalent to the square root of three times our times t divided by em are is simply a constant. Tia's are temperature and m is are more massive helium. We'll get that C is equivalent to three times 8.314 which is is the value of the constant are times 500 divided by four times 10 to the negative third and remember, this entire fraction is inside the square root and we do that we'll get that C is equivalent to the square root of three million, 101. My apologies. Three million, 117,750 jewels per kilograms and we simplify that square root will get that. The root mean square of helium is 1.765 times 10 to the third meters per second. Now for B. If we want to know the wavelength wavelength is equivalent to H about it by M times C where h is Planck's constant C is mass or part of me. M is mass and C is our speed of light. We'll get that lambda our wavelength is equivalent to Plank's constant 6.626 times 10 to the negative 34th Jewell seconds Divided by R Mass four times 10 to the negative third kilograms per mole multiplied by the speed of light three times 10 to the eighth meters per second. Now, in order for these units to cancel will have to multiply by a conversion factor. I don't multiply by 1 g, multiplied by meters squared per second and everyone Jewell And then when we simplify, this will get at Lambda is equivalent to 0.5525 times 10 to the negative fourth meters. But we normally described wavelength using nano meter so we can convert that to get that our wavelength is 0.5525 times 10 to the negative 31st Nana leaders.

So this question belongs to the kinetic theory of gases, in which we have to determine the temperature T at which the root mean square speed of an atom in organ guests. That is uh temperature. Organ we have to determine here actually is equal to the RMS speed. We are a mess of argon. This has been equals two. We are a mess of the helium gas at the temperature, the temperature of the helium, it is given as minus 20 degrees, integrate that is equals 2 to 53 Calvin. Okay, so we know that the V. RMS it is equals two and the root of three RT divided by molecular weight. M Okay, so since we are M. S. Is equal for the boat, so hence temperature is directly proportional to molecular weight from here. Okay, so we can write temperature helium two divided by temperature Organ this is equal to molecular weight of helium to the molecular weight of organ. Okay, so after solving a equation, temperature, Organ comes out to be molecular weight of organ divided by molecular weight of helium, declared a temperature of helium. So substituting values the temperature of organ gas is equal to molecular weight of organ. This is equal to 39.9 which is given you the whereby molecular weight of helium, which is given as 4.0. You are cleared. The temperature of the helium which is 2 53 Calvin. Okay, so from here after solving uh we will get that this temperature, it is equal to 2.52 molecular by 10 to the power three Calvin. So hence we can write the temperature of the organ. This is equal to 2.53 or 2.5 to 3, multiplied by 10 to the power three Calvin. So that's become the answer for this problem. Okay, thank you.

Hello students. In this question we have given a sample of helium gas at temperature equals to 300 Calvin and pressure p equals to 0.5 80 M. So we have to calculate the average kinetic energy of the molecules of gas. So we know that the average kinetic energy of molecules it is equal to the half by two Katie where small life is the degree of freedom. And for the helium guests that is mono atomic degree of freedom is three. So this is equal to three by two K. T. Where K. Is the Goldman constant and T. Is the absolute temperature. So substituting values. So kinetic energy average will be equals to three by two medical herb. Okay. Which is one country at molecular by 10 to the power minus 23 jewel per kelvin molecular be absolute temperature is 300 Calvin. So from here we get average kinetic energy of the molecules. This is equal to 6.21 molecular between 10 to the power managed 21 jewel. Okay, so that's become the answer for this question. Okay, thank you.


Similar Solved Questions

5 answers
Compute the probability: (a) If P(A) 0.75, P(B) 0.4 P(A and (c) If P(A) = 0.35, find P(Ac). and B) = 0.25, find P(A or B)(d) If P(A:) = 0.27 , find P(A): (6) If P(A) 0.2, P(B) 0.5, and A &nd B are mutually exclusive; find P(A or B)
Compute the probability: (a) If P(A) 0.75, P(B) 0.4 P(A and (c) If P(A) = 0.35, find P(Ac). and B) = 0.25, find P(A or B) (d) If P(A:) = 0.27 , find P(A): (6) If P(A) 0.2, P(B) 0.5, and A &nd B are mutually exclusive; find P(A or B)...
5 answers
The 1H-NMR and 13C-NMR spectra of an unknown compound (formula CsHio) are shown below. Draw the structure of the unknown compound: The total integration of the peaks at around ppm is The integration of the peak at around ppm isppmZ0018016014012010080pm
The 1H-NMR and 13C-NMR spectra of an unknown compound (formula CsHio) are shown below. Draw the structure of the unknown compound: The total integration of the peaks at around ppm is The integration of the peak at around ppm is ppm Z00 180 160 140 120 100 80 pm...
5 answers
"uoiijeaj shown product formation from the al reagent(s) that would lead lo the { BH3 in THF 1 H20z/H20 GUESTION Choose 02
"uoiijeaj shown product formation from the al reagent(s) that would lead lo the { BH3 in THF 1 H20z/H20 GUESTION Choose 02...
5 answers
Amotal-plating conpany Donone #talistcal ilornialion aboui inis poct3tIninonFncon70382e udrpom Er botgOvorall Avotape Maan: Owamll Slanderd Duadneae25874 0=1,.285 nesSampln St4= Fnnd the LCLPoinia)Find bto UCL, (5 Polnte)Fid ta UCL, (5 Points)Find 170 LCL, (5 Poib}
Amotal-plating conpany Donone #talistcal ilornialion aboui inis poct3t Ininon Fncon 70382e udrpom Er botg Ovorall Avotape Maan: Owamll Slanderd Duadneae 25874 0=1,.285 nes Sampln St4= Fnnd the LCL Poinia) Find bto UCL, (5 Polnte) Fid ta UCL, (5 Points) Find 170 LCL, (5 Poib}...
5 answers
VIA, B are sets, prove that (AnBJU(AnB) = A (Use Latex to typeset your proof and state which Identity of set using In each step)
VIA, B are sets, prove that (AnBJU(AnB) = A (Use Latex to typeset your proof and state which Identity of set using In each step)...
5 answers
Solve the heat equation Ut 5uxx 6ux' 0 < x < T,t > 0 u(0,t) = u(i,t) = 0 t > 0 u(x,0) = sin (x) 0 < * < T
Solve the heat equation Ut 5uxx 6ux' 0 < x < T,t > 0 u(0,t) = u(i,t) = 0 t > 0 u(x,0) = sin (x) 0 < * < T...
5 answers
14_ Draw a detailed arrow-pushing mechanism for the following tra :Cl: ACl3 ~AClA
14_ Draw a detailed arrow-pushing mechanism for the following tra :Cl: ACl3 ~AClA...
5 answers
The atmospheric pressure at altitude, h in kilometers, for 11 < h < 25 is approximately P(h) = 128e -157h kilopascals. Estimate AP at h = 20 when Ah =.5 Compute the actual change and compute the percent error in the Linear Approximation.Find the minimum and maximum value ofy = x - [0, 3] by comparing values at the X+ critical points and endpoints_
The atmospheric pressure at altitude, h in kilometers, for 11 < h < 25 is approximately P(h) = 128e -157h kilopascals. Estimate AP at h = 20 when Ah =.5 Compute the actual change and compute the percent error in the Linear Approximation. Find the minimum and maximum value ofy = x - [0, 3] by c...
4 answers
Find rarefaction wave solution; i.e., u(z,t) 9(5-8), of the following initial value problem: Ut + (u2 + l)ur 0. O0 <1 < 0, t > 00 X<-1u(z,0) =1 >-1.
Find rarefaction wave solution; i.e., u(z,t) 9(5-8), of the following initial value problem: Ut + (u2 + l)ur 0. O0 <1 < 0, t > 0 0 X<-1 u(z,0) = 1 >-1....
5 answers
Penicillins are eta-lactam ring containing compounds. Give general structure of penicillins and indicate the $eta$ -lactam portion of the structure by encircling it.
Penicillins are \beta-lactam ring containing compounds. Give general structure of penicillins and indicate the $\beta$ -lactam portion of the structure by encircling it....
1 answers
In 1999 , an unusual cation containing only nitrogen $\left(\mathrm{N}_{5}^{+}\right)$ was prepared. Draw three resonance structures of the ion, showing formal charges. (Hint: The $\mathrm{N}$ atoms are joined in a linear fashion.
In 1999 , an unusual cation containing only nitrogen $\left(\mathrm{N}_{5}^{+}\right)$ was prepared. Draw three resonance structures of the ion, showing formal charges. (Hint: The $\mathrm{N}$ atoms are joined in a linear fashion....
5 answers
4vae/ Pallei Ctoss $ciioks Culns 42 X= (6-4) Ma4Ve (@Sc 4-264+71dy 3'/6 4 [k- K 6y-kyt+ +6] KL '0 f Oa >ua lles | Sof t will f,t io Fyraud 5, 3 Ve(uue orrer Va1v4 Utlec Sum 0 6 V-L~ 6-/2 > ull Ov € 804 8 ( Ve(Jite $ 0 f Qela e Alete e4 24 L Pyreuid Iah Ud I_ Pyveutid Ft Li=0 0 < $ a'k < 0 U. a4 Li= 6 + al al Uz = 044 4 Lzs @ ('.84 {a"a%a"k 8 Uz = L4 = CL 0+4"+ 243*] 30474] 10k5 gat? 4at 4(4 ) 04 = ak 'Li"+2' '+3+4']= ( 4 U
4vae/ Pallei Ctoss $ciioks Culns 42 X= (6-4) Ma4 Ve (@Sc 4-264+71dy 3'/6 4 [k- K 6y-kyt+ +6] KL '0 f Oa >ua lles | Sof t will f,t io Fyraud 5, 3 Ve(uue orrer Va1v4 Utlec Sum 0 6 V-L~ 6-/2 > ull Ov € 804 8 ( Ve(Jite $ 0 f Qela e Alete e4 24 L Pyreuid Iah Ud I_ Pyveutid Ft Li=0 0...
1 answers
1 Prove that X'X is positive definite if X is of full column rank: Hint: What needs to be shown is that cX'Xc 0 for 7 0. Define = Xc_ Then cXXc = zz = Ck_1=%. If Xis of full column rank, then z # 0 for any € = 0. 2 Verify that XX/n Zi Xjx; and Xy/n Li Xi . Ji as in (1.2.6). Hint: The (k, €) element of X'X is Ci XikXie .
1 Prove that X'X is positive definite if X is of full column rank: Hint: What needs to be shown is that cX'Xc 0 for 7 0. Define = Xc_ Then cXXc = zz = Ck_1=%. If Xis of full column rank, then z # 0 for any € = 0. 2 Verify that XX/n Zi Xjx; and Xy/n Li Xi . Ji as in (1.2.6). Hint: The...
5 answers
In an attempt t0 measure the effects of acid rain; researchers measured the pH (7 is neutral and values below are acidic) of water collected from rain in Ingham County; Michigan:5.475.375.384.635373.743.714.96 4.645.11 5.65 5.394.16 5.62 4574.645.48 4.574574.5[ 4.86 4.56 4.61432 3.98 5.70 +15 3.98 5.65 3.10 5.044.62 4514.344.464.645.123.71 4.645.59
In an attempt t0 measure the effects of acid rain; researchers measured the pH (7 is neutral and values below are acidic) of water collected from rain in Ingham County; Michigan: 5.475.375.384.635373.743.714.96 4.645.11 5.65 5.394.16 5.62 4574.645.48 4.574574.5[ 4.86 4.56 4.61432 3.98 5.70 +15 3.98 ...
5 answers
This Question: ptDetermine whether the quantitative variable is discrete or continuous_Running time of music fileIs the variable discrete or continuous?The variable continuous because it Is not countable_ The variable is continuous because it is countable. The variable Is discrete because it is countable. Tne variable is discrete because it Is not countableClick ' select your answer:
This Question: pt Determine whether the quantitative variable is discrete or continuous_ Running time of music file Is the variable discrete or continuous? The variable continuous because it Is not countable_ The variable is continuous because it is countable. The variable Is discrete because it is ...
5 answers
Find y at the specified point.16 ' at (5,1)I + y
Find y at the specified point. 1 6 ' at (5,1) I + y...

-- 0.022212--