volume of helium in a balloon

Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The molar volume is the volume occupied by one mole of a gas at a particular temperature and pressure. The following charts should help you. Can airtags be tracked from an iMac desktop, with no iPhone? Seriously, it is only slightly higher than atmospheric pressure. Where does this (supposedly) Gibson quote come from? Which differs slightly from our previous result based on the $30$km buoyancy calculation due to inaccuracies in the air density value at $30$km. Making statements based on opinion; back them up with references or personal experience. And how much helium do you need according to the mass that the balloon has to carry? 2023 BrainRouter LTD. All rights reserved. (326g) *Because the filling and usage of display balloons is beyond our control, no performance or longevity guarantee can be made. Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form. The output density is given as kg/m 3, lb/ft 3, lb/gal (US liq) and sl/ft 3 . How to prove that the supernatural or paranormal doesn't exist? How do you get out of a corner when plotting yourself into a corner, Is there a solutiuon to add special characters from software and how to do it, Styling contours by colour and by line thickness in QGIS. Since the temperature and mass of the gas is constant during the process, and helium can be considered as ideal gas, we can apply the BoyleMariotte law (see https://en.wikipedia.org/wiki/Boyle%27s_law): where "P_1 = 100000Pa, V_1 = 0.030m^3" are the pressure and volume before the compression respectively, and "P_2, V_2 = 0.025m^3" are the pressure and volume after the compression respectively. View Screen Shot 2023-03-02 at 3.04.07 PM.png from CHEM 00808 at Rowan University. In this case, since the volume and molar quantity of the gas are changing, you need to solve the following equation: So, for this particular problem: 0.8323 L = 4.266 L. n 1 20.4 mol, or n 1 = (20.4) (0.8323) 4.266, or n 1 = 3.98 mol of helium initially. \end{align}, $$V = \frac{m_\text{payload}RT}{P(M_a - M_h)} \tag{2}\label{2}.$$. I start from the Buoyancy Formula: Helium balloons float because helium is less dense than air. Special Offer on Antivirus Software From HowStuffWorks and TotalAV Security. ncdu: What's going on with this second size column? Density of Helium = .18 kg/m 3. The air in the tube is initiall, The cylinder of a pump has a volume of 25.0 cm3. However, do we need any density measurement at all? 0.336 L volume of the balloon? Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. Choose the actual unit of temperature: C F K R. Is it correct to use "the" before "materials used in making buildings are"? Mass lifted = mass of the volume of fluid displaced. Anagram is the worlds largest manufacturer of foil balloons for every occasion; 18-inch, large shapes, singing, recordable, licensed characters, custom, decorator and other specialty balloons /> supplies, kids birthday party, kids parties, decoration party, baby shower decorations, ballons, balloon shop, party decor, helium balloon, party balloons, helium balloons, latex balloons, party . Well, in the limiting case, the upthrust force will just balance the weight of the balloon, so we can say that: \begin{align} Your local, ARA-affiliated rental store professionals also can assist you in renting the proper helium tank. Expert Answer. Here is how you can figure out the lifting capacity of the helium in a spherical helium balloon: So, for example, a 20-foot balloon has a radius of 10 feet. The ideal gas law describes how the volume of a gas varies with amount, in mol, of gas particles, pressure, and temperature. The following chart breaks down nearly a dozen different sizes of helium cylinders. Alternatively, we could calculate the amount of gas in the initial volume at sea level ($4.71\text m^3$) and then see what volume this amount of gas would occupy when subjected to the higher pressure and lower temperature at $30$km. Connect and share knowledge within a single location that is structured and easy to search. $$M = m_\text{payload} + m_\text{helium}$$. (1) The pressure of helium in each balloon is 1.1 10 5 Pa. The volume of the balloon is 0.030m ^3. Specific weight is given as N/m 3 and lb f / ft 3. To determine how much helium gas we need, we need to consider the necessary buoyancy required. Find step-by-step Chemistry solutions and your answer to the following textbook question: A weather balloon is filled with helium that occupies a volume of $5.00 \times 10^{4} L$ at 0.995 atm and $32.0^{\circ} \mathrm{C}$. The input parameters are; temperature, balloon mass, payload mass, initial diameter and max diameter. This is only slightly larger than the surrounding air (atmospheric) pressure due to any surface tension in the balloon, so we can take the two to be roughly equal. ; Washington, DC 20230. han LooL Enter number of moles and select a substance to search for. Note that the pressure was converted from kPa to Pa, and the molar mass from gmol$^{-1}$ to kgmol$^{-1}$. (If you're sceptical, I checked Equation \ref{1} with these calculations.). The ascent-rate is velocity where the buoyancy (force) of the . There are 249.81 decimoles in 100 grams of Helium. That is a. The helium in the cylinder has a volume of 6.0 10^-3 m3^-1 (0.0060 m^3) and is at a pressure of 2.75 10^6 Pa. (i) The pressure of helium in each balloon is 1.1 10^5 Pa. A balloon is a flexible bag that can be inflated with a gas, such as helium, hydrogen, nitrous oxide, oxygen, and air.For special tasks, balloons can be filled with smoke, liquid water, granular media (e.g. MathJax reference. A bicycle tyre has a volume of 1.2 x 10-3 m3 when fully inflated. At sea level, the external atmospheric pressure of the air is equal to 14.7 lbs/in 2 or 1.0135 bar or 1 atm (those three values are all equal just like 1 yard is equal to 0.9144 meters). (Because gas molecules interact with each other in ways different from purely elastic collision, gases do . Or am I overthinking this? Volume of Helium in Different Sizes. There are three certainties in this world: Death, Taxes and Homework Assignments. So we should get the same volume if we fill the balloon with ordinary air and hoist it into the atmosphere mechanically instead of letting it rise by its own buoyancy. A few materials, substances, compounds or elements with a name containing, like or similar to. I think they're mainly used for research and etc. \end{align}. , where k is a constant for any given temperature and pressure. 1. Going back to Equation \ref{1} Let's face it, that equation is ugly. Fill the balloon with air. Density of Air = 1.3 kg/m 3. How can I determine whether balloons inside a balloon are filled with the same gas? The mass and volume of helium in the balloon remained constant. Then, under water, let the air escape into an inverted bottle that has been filled with water. PV &= nRT \\ Asking for help, clarification, or responding to other answers. According to this source, the temperature at sea level is $15.0$C $ \approx 288.2$K, the pressure is $101$kPa, and the density is $1.23\text{kg}\text{m}^{-3}$. Our experts will gladly share their knowledge and help you with programming projects. Burst Altitude: 35.000 - 36.000 m. Ascent Rate: 5.00 m/s. Note that this assumes the air behaves ideally (obeys $PV = nRT$), and, as we said before, the balloon exerts no additional pressure on the helium gas (if we had a metal balloon, the buoyancy would decrease with altitude of course since the volume of helium would be fixed but the air density would be decreasing). \implies n &= \frac{PV}{RT} 1.00 kg of neon gas has, 80.0 cm3 of hydrogen is collected during a chemistry experiment at 20.0C and 101 kPa. Take a look at the ideal gas law and Archimedes' principle. A uniform electric field with a magnitude of 6.8 x 104 N/C is passing through a flat square with, Problem Solving:1. Use MathJax to format equations. Knowing the volume of air displaced by the helium balloon, we can calculate the maximum mass the balloon can lift. Furthermore, I also have noticed that because of the lower pressure higher in the atmosphere helium expands and balloon seems filled up. Which we can re-arrange for the volume of helium: $$V = \frac{m_\text{payload}}{\rho - \frac{PM_h}{RT}}\tag{1}\label{1}$$. A balloon is filled with 1.50 L of helium gas at sea level, 1.00 atm and 32C. We've added a "Necessary cookies only" option to the cookie consent popup. About Helium. A helium balloon ride lifts up passengers in a basket. )What distance does the ga, In case of average velocity a body may followStraight pathCurved pathVariable motionAll of them, A cart is at x = 5.25m and time t = 0. Why do helium balloons expand in volume as they go higher? Balloon is compressed at a constant temperature causing the volume to decrease to 0.025m^3. Balloon is compressed at a constant temperature causing the volume to decrease to 0.025m^3. If an air mass started to rise then contract due to cooling, that would be the end of that convection event. The upthrust is determined by the volume of the object (in this case the volume of the air balloon), and the density of the fluid (here the density of the air at different altitudes). So I've seen those big helium balloons that are not even filled all the way up, but they still manage to reach heights of up to 30 km. Steps to complete the problem: List all of the variables given. Also provided is the volume of helium that should be used for each size and type of balloon, all the way up to massive 40 . It depends on the size of the balloon. I didn't know that balloons expanded during the fly because of thermodynamics, and I didn't know how high they can fly, but a rapid search tells that a partially unfilled regular balloon can fly until an altitude of around $\pu{25 km}$. (the molar heat capacity for helium gas is 20.8 j/c # mol.) There is something incredibly neat about helium balloons! answered 04/17/20. The most straightforward approach would be to sub-in the conditions at an altitude of $30$km to Equation \ref{1}. What is precisely the reason that a helium balloon ascends? If you preorder a special airline meal (e.g. density of helium is equal to 0.1785 . One balloon contains 1.0 g helium. But at the same time, doesn't the outside temperature decrease, causing the gas particles in the balloon to lose energy and have less impactful collisions and a lower velocity? Calculate the balloon's lift weight by multiplying the volume by the mass a liter of helium can lift 1.0715 g . And how much helium do you need according to the mass that the balloon has to carry? Number mol. sand, flour or rice), or light sources.Modern day balloons are made from materials such as rubber, latex, polychloroprene, or a nylon fabric, and can come in many different colors. They have fewer electrons, protons and neutrons than nitrogen atoms do, and that makes them lighter (the approximate atomic weight of hydrogen is 1, helium is 4 and nitrogen is 14). That was very helpful! How to react to a students panic attack in an oral exam? In the film we see an enormous collection of balloons above the house, perhaps 10 times the volume of the house. It only takes a minute to sign up. Mass = (1200 m 3 ) ( 1.3 kg/m 3) On a nice, clear, dry 25C day at sea level, atmospheric pressure decreases by about 12% per km, where the air temperature decreases by about 3% per km. Learn more about our help with Assignments: Thank you! What is the lifting force of in kN for a 10 m diameter spherical balloon with helium inside at 101 kPa and 320 K surrounded by air at 101 kPa and 298.15 K? Take into account that normal atmospheric pressure at sea level is also about 1.1 x 10^5 Pa. 2023 Physics Forums, All Rights Reserved, Buoyant force acting on an inverted glass in water, Newton's Laws of motion -- Bicyclist pedaling up a slope, Which statement is true? Adding helium to a balloon increased its volume from 832.3 mL to 4.266 L. If the final number of moles of helium in the balloon is 20.4 mol, what was the initial number of moles of helium in the balloon? In this case, the helium balloon that you hold by a string is floating in a "pool" of air (when you stand underwater at the bottom of a swimming pool, you are standing in a "pool of water" maybe 10 feet deep -- when you stand in an open field you are standing at the bottom of a "pool of air" that is many miles deep). Time to Burst: 120 min. Math behind helium balloons lifting objects to (almost) space, We've added a "Necessary cookies only" option to the cookie consent popup. Thanks for contributing an answer to Physics Stack Exchange! If you buy one at the circus or fair, you can hold its string and it will ride along above you. Subscribe Now:http://www.youtube.com/subscription_center?add_user=ehoweducationWatch More:http://www.youtube.com/ehoweducationMeasuring the volume of helium in a balloon is something that you can easily do with two different techniques. Note that the gas pressure is of the helium in the balloon. The helium is irrelevant. The barrel of the pump has a wor, Neon is a monatomic gas, in which inter-molecular forces are extremely weak. 3-5 days. The N, R and P do not change in helium and hot air balloons, only volume and temperature. I realize as balloons go higher, the atmospheric pressure decreases, doing less to counteract the force of the gas particles pushing against the inner walls of the balloon. Pressure Cooker at High Altitudes and Low Altitudes, Dissociation of phosphorus pentachloride in gas syringe, "We, who've been connected by blood to Prussia's throne and people since Dppel", Theoretically Correct vs Practical Notation. Explain why the pressure exerted by the helium inside the balloon would increase. # per Avg. And to convert from moles to mass we use the molar mass of helium, $M_h = 4\text g \text{mol}^{-1}$, to give that, $$m_\text{helium} = n\cdot M_h = \frac{PVM_h}{RT}.$$, $$m_\text{payload} + \frac{PVM_h}{RT} = V\rho.$$. 7. The ideal gas law, PV = nRT, gives the relationship among pressure, volume, temperature and number of moles (n) for a gas. (Consider what happens if we compress a portion of air with a piston -- say, a bicycle pump. 4. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. Divide by 448 -- the number of grams in a pound . It only takes a minute to sign up. 3' 30" 18" 16" 11" 5" 16" Helium Capacity 1.5 cu. However, they need to be checked by the moderator before being published. To learn more, see our tips on writing great answers. You are holding two balloons of the same volume. Science Chemistry 9. All Qualatex latex balloons are helium-weight quality and are manufactured in the USA or Canada from 100% natural, biodegradable latex. Answer: When you say "how much", and "lift" practically what you mean is "What VOLUME of He at atmospheric pressure will lift a given object using a conventional baloon-like contraption. How can I explain to my manager that a project he wishes to undertake cannot be performed by the team? A: Given : Load mload=100 kg Helium density helium =0.179 kg /m3 Air density air=1.29 kg /m3. However, they need to be checked by the moderator before being published. Asking for help, clarification, or responding to other answers. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning, a Question If you have ever wondered why it flies away, then read on. Before you rent a helium tank, know how many balloons you will need, so you can determine the size of tank you will need to rent. Cube the radius (multiply it by itself twice: r*r*r), multiply by 4/3 and then multiply by Pi. Determine the volume of the balloon. The temperature of the helium in the balloon was increased. Note that I will use $B$ for buoyancy (upthrust) so as to not get confused with $T$ for temperature. You are using an out of date browser. Your comments have been successfully added. Learn more about our help with Assignments: Thank you! Very interesting problem, and a nice result at the end too! Since each helium balloon creates about 10 g of lift you would need at least 10 000 000/10 balloons - ie about a million balloons to lift the house! How do you actually find maximum volume of the balloon according to the height that it has to reach and temperature at that height? In this edition of HowStuffWorks, you'll find out all about helium! for any assignment or question with DETAILED EXPLANATIONS! It was, and is still being, formed from alpha-particle decay of radioactive elements in the Earth. Heating the gas, we increase the speed of its molecules. How do you actually find maximum volume of the balloon according to the height that it has to reach and temperature at that height? Give your answer to two decimal places. For each size tank, we tell you how many balloons you can fill for each size of balloon, from 9-inch latex to 18-inch foil/mylar balloons. How to keep a helium balloon between 1 to 5 meters above ground? Question: A helium balloon, assumed to be a perfect sphere, has a radius of 24.0 cm. However, it is highly flammable, so the slightest spark can cause a huge explosion. Last accessed: 29 August 2020 (nist.gov). Use * as a wildcard for partial matches, or enclose the search string in double quotes for an exact match. The best answers are voted up and rise to the top, Not the answer you're looking for? The volume of the balloon is ( V) = 217 .03 L. See the step by step solution. It is connected to a container of volume 225 cm3, c. PV &= nRT \\ Enter weight, select a unit of weight, and specify a material or substance to search for. Nitrogen weighs 1.2506 grams per liter, and since nitrogen makes up about 80 percent of the air we breathe, 1.25 grams is a good approximation for the weight of a liter of air. "P_2 = \\dfrac{P_1V_1}{V_2}\\\\\nP_2 = \\dfrac{100000Pa\\cdot 0.030m^3}{0.025m^3} = 120000Pa", Two protons in an atomic nucleus are typically separated by a distance of 2 x 10-15 m. The electric, How much work is done on a table pulled 5m by a force of 30N at an angle of 60 above the horizonta, A gardener walks in a flower garden as illustrated in the figure below. . Learn more about Stack Overflow the company, and our products. Now, we can just plug all of these values in and solve for V: So why are helium and hydrogen so much lighter than air? It turns out that helium is a lot lighter than air. Assuming no change in pressure or in temperature reduces this problem to. Why do small African island nations perform better than African continental nations, considering democracy and human development? V &= \frac{m_\text{payload}}{\rho - \frac{PM_h}{RT}} \\ Rent the Right Size of Helium Tank. Please copy/paste the following text to properly cite this HowStuffWorks.com article: Marshall Brain A weather balloon contains 8.80 moles of helium at a pressure of 0.992 atm and a temperature of 25 C at ground level. Divide by 448 -- the number of grams in a pound -- to determine the number of pounds it can lift. Also, if the density were the same everywhere, air at sea level would not be compressed by the weight of the atmosphere above us, which is also absurd. What is the electric field strength at a point that is 0.25 m to the lef. Temperature effect of rising helium balloon in air. Neck Lift: 2715 g. Volume: 4232 L If you use one 20L gas bottle with 200 bar filling pressure: 235 Bar Two bottles are needed. Since the balloon's volume is not changing, we know that the outside pressure on the balloon is balanced . What video game is Charlie playing in Poker Face S01E07? Assuming that no helium escapes from the balloon in that time, will the balloon have a larger volume than, a smaller volume than, or the same volume as that it had on the previous day? 9. So how large will the balloon be at its peak? So, this is an application of Avogadro's law (which is derived from the ideal gas law or PV = nRT where P is the gas pressure, V is the volume occupied by the gas, n is the moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin). Thus, expressing "P_2", obtain: for any assignment or question with DETAILED EXPLANATIONS! What is its, A steel thick-walled gas cylinder used for storing compressed air is fitted with a safety valve whi, 2. 4,186 cubic feet * 28.2 grams/cubic feet = 118,064 grams. The temperature of the helium does not change. 118,064 grams / 448 grams per pound = 263 pounds of lifting force. To learn more, see our tips on writing great answers. Use MathJax to format equations. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. A limit involving the quotient of two sums. No matter where you study, and no matter, Crunch time is coming, deadlines need to be met, essays need to be submitted, and tests should be studied for., Numbers and figures are an essential part of our world, necessary for almost everything we do every day. Answer (1 of 3): If it is filled with air, it is about 950 millibars plus or minus 75 millibars. Helium weighs 0.1785 grams per liter. Keep up with the worlds newest programming trends. Doubling the cube, field extensions and minimal polynoms, ERROR: CREATE MATERIALIZED VIEW WITH DATA cannot be executed from a function. $= 8.314\text{J}\text{mol}^{-1}\text{K}^{-1}$. What video game is Charlie playing in Poker Face S01E07? Thanks for contributing an answer to Chemistry Stack Exchange! Why are Suriname, Belize, and Guinea-Bissau classified as "Small Island Developing States"? Assume the balloon contained only helium initially. A second balloon at the same temperature and pressure has a volume of 18 liters. 15 cu ft (.425m3) 3-5 days. Your physics assignments can be a real challenge, and the due date can be really close feel free to use our assistance and get the desired result. The best answers are voted up and rise to the top, Not the answer you're looking for? Archimedes' principle allows you to calculate the upthrust on an object in a fluid (a liquid or gas). (without it being tied). Can I tell police to wait and call a lawyer when served with a search warrant? The volume is then: Volume (cm^3) = Weight(gm)/1(gm/cm^3), (neglecting the weight of the empty balloon.) 0.0001785 gram [g] of Helium fits into 1 cubic centimeter, 0.00010318 ounce [oz] of Helium fits into 1 cubic inch, A few materials, substances, compounds or elements with a name containing, like or similar to. How do you get out of a corner when plotting yourself into a corner. The mass of the helium can be calculated from the number of moles which we can calculate using the ideal gas equation: \begin{align} No helium leaves the balloon. HELIUM & WEIGHT CHART A balloon filled with helium gas takes 3.96 hours to deflate to 25.1% of its original volume. = 6.00 g 4.00 g/mol = 1.50 mol. How is Jesus " " (Luke 1:32 NAS28) different from a prophet (, Luke 1:76 NAS28)? After it is released, it rises to a location where the pressure is 0.720 atm and the temperature is $-12.0^{\circ} \mathrm{C}$. Calculate the number of balloons that were . vegan) just to try it, does this inconvenience the caterers and staff? No packages or subscriptions, pay only for the time you need. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. If The speed of the cart, 1. Method 2. You should be able to calculate the volume of helium at high and low altitudes by searching for the pressures and temperatures at those locations. No helium leaves the balloon. Compute the volume of the balloon, approximating it to a sphere with a radius r = 11"/2 = 13.97 cm. This explains why blimps and balloons are generally quite large -- they have to displace a lot of air to float. This is because the volume of the balloon increases in proportion to the temperature and inversely proportional to the atmospheric pressure, whereas the density of the air increases proportionally to the atmospheric pressure and inversely proportionally to the temperature, so that they cancel out. The buoyant force will be the weight of air that it displaces because that's Archimedes principle, and the weight of the air displaced will be the mass of the air times g.So let's create an expression for the mass of the air in terms of volume because we know the . The physics behind Balloons lifting objects? Assume the balloon contained only helium initially. volume: V = 4/3 r = 4/3 13.97 = 11420.3cm = 11.420 L. mass: m = 11.420 L 1.0715 g/L . And although this data is readily available, as we have found, it is not all that accurate. This is assuming that no helium escapes the balloon. Use * as a wildcard for partial matches, or enclose the search string in double quotes for an exact match. \implies \frac{n}{V} &= \frac{P}{RT} \\ 1.0 g 4.0 g d. 5.0 g e. 20. g a. Weod 0.25mol dog I mol . Now how can we use this to calculate the volume of helium gas? From the moment a white orb was spotted floating 60,000 feet over Montana, people on Twitter and cable news demanded the Biden administration shoot it down. Most questions answered within 4 hours. Helium balloons deflate because helium atoms are small enough to slip between spaces in the balloon material. The radius of the balloon (when filled) is R = 5.3 m. The total mass of the empty balloon and basket is mb = 129 kg and the total volume is Vb = 0.057 m3. What am I doing wrong here in the PlotLegends specification? Connect and share knowledge within a single location that is structured and easy to search. Calculate the new pressure in the balloon. Over time, however, the helium will leak from the balloon and the balloon will shrink. About Helium; Helium weighs 0.0001785 gram per cubic centimeter or 0.1785 kilogram per cubic meter, i.e. Keep up with the worlds newest programming trends. Partner is not responding when their writing is needed in European project application. A balloon filled with 39.1 moles of helium has a volume of 876 l at 0.0'c and 1.00 atm pressure. Technically once we calculate the amount of helium in the balloon at sea level, we only need readings for temperature and pressure at the higher altitude, not density, as we saw in the second calculation which lead to $312\text m^3$. Adding helium to a balloon increased its volume from 315.0 mL to 2.199 L. If the final number of moles of helium in the balloon is 26.9 mol, what was the initial number of moles of helium in the balloon? Note: The results calculated with the helium calculator are only approximate values and may deviate from reality due to the influence of . Because helium is lighter that air, a helium balloon rises, just as an air bubble rises in more dense water. Since we are already assuming that the air in the atmosphere behaves as an ideal gas, we do not. If you let go of the string, it will fly away until you can't see it anymore. @EIMA I've added full equation details and some example data for you to take a look at. The attachment is either tied into the knot, or secured with a plastic disk. A ballon filled with 1lb of helium weighs 1lb+ the ballon. Helium is deemed to be worth . Helium is a gas like air; in fact, air has some helium in it. Q: How many cubic meters of helium are required to lift a light balloon with a 370-kg payload to a. rev2023.3.3.43278. We can express this total mass as that of the helium gas and that of the payload. \begin{align} The density of hydrogen gas at 0C and IUPAC standard pressure (100 kPa) is 9.00 g/m3. $$n = \frac{PV}{RT} = \frac{101 \times 10^3 \times 4.71}{8.314 \times 288.2} = 199\text{mol}.$$. 0.00010318 ounce [oz] of Helium fits into 1 cubic inch. If you try a $pV=nRT$ calculation on these data, you see that the gas is already at around 10 times its initial volume with $\pu{40 mmHg}$ pressure and a $\pu{213 K}$ temperature, and that at the $\pu{50 km}$ point the volume is increased 700 times!

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