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Suppose we wish to inflate a weather balloon with helium. The balloon should have a volume of \(100 \mathrm{~m}^{3}\) when inflated to a pressure of \(0.10\) bar. If we use \(50.0\) -liter cylinders of compressed helium gas at a pressure of 100 bar, how many cylinders do we need? Assume that the temperature remains constant.

Short Answer

Expert verified
20 cylinders are needed.

Step by step solution

01

Understand the Problem using Ideal Gas Law

We need to find out how many helium gas cylinders are required to fill the balloon to a certain volume and pressure. Since the temperature is constant, we can use the Ideal Gas Law, which is given by \[ PV = nRT \]where \(P\) is the pressure, \(V\) is the volume, \(n\) is the number of moles, \(R\) is the gas constant, and \(T\) is the temperature.
02

Calculate the Moles in the Balloon

First, find the number of moles of helium needed for the balloon (volume = 100 m³ at 0.10 bar). Using the Ideal Gas Law:\[ PV = nRT \]First, convert the volume to liters: 100 m³ = 100,000 liters. Now solve for \(n\):\(n = \frac{PV}{RT}\). Omitting \(R\) and \(T\) (as we are only interested in ratios):\(n_1 = \frac{0.10 \times 100,000}{RT}\).
03

Calculate the Moles in One Cylinder

Now, calculate the number of moles in a 50-liter cylinder at 100 bar using the Ideal Gas Law:\[ PV = nRT \]Convert the volume to meters cubed for consistency. Since we need only a ratio, we can use:\(n_2 = \frac{100 \times 50}{RT}\).
04

Calculate the Number of Cylinders Needed

To find the number of cylinders, divide the total moles needed for the balloon by the moles available per cylinder:\[ \text{Number of cylinders} = \frac{n_1}{n_2} \]Substituting in the simplified relation:\[ \frac{0.10 \times 100,000}{100 \times 50} = 20 \]Thus, we need 20 cylinders.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Helium Gas
Helium is a noble gas, which means it's very stable and doesn't easily react with other elements. As a non-toxic, colorless, odorless gas that's much lighter than air, helium is perfect for inflating weather balloons.
Its lightness allows the balloon to float high into the atmosphere. Being less dense than air helps provide the lift.
Helium doesn't condense easily under standard conditions, making it one of the preferred choices for such applications.
  • Helium is an inert gas, ensuring that there’s no reactive danger involved.
  • Due to its low density, helium provides the necessary buoyancy.
  • It remains gaseous at lower temperatures, which is crucial as temperatures drop when moving higher in the atmosphere.
These characteristics make helium not only safe but also efficient for filling balloons that are intended to reach high altitudes. Understanding these properties helps us appreciate why helium is the gas of choice for weather balloons rather than more reactive or denser gases.
Purpose and Functionality of Weather Balloons
Weather balloons are critical tools used by meteorologists to collect data about atmospheric conditions. They carry instruments called radiosondes that measure a variety of weather data.
As the balloon ascends, it collects information like temperature, pressure, and humidity, sending this data back to ground stations for analysis.
The data collected is vital for weather forecasting, climate studies, and even emergency situations.
  • Weather balloons provide real-time data on atmospheric conditions.
  • Their instruments help in understanding and predicting weather patterns and phenomena.
  • The balloons reach altitudes where airplanes do not fly, offering unique insights.
By inflating weather balloons with helium, they can rise thousands of meters into the atmosphere, offering detailed profiles of upper-level weather conditions. Additionally, understanding the Ideal Gas Law enables engineers to efficiently calculate how many helium gas cylinders are needed for inflation, ensuring optimal performance and reliability of the balloons.
The Role of Gas Cylinders in Weather Balloon Inflation
Gas cylinders are crucial in the process of weather balloon inflation. They store large amounts of helium gas under high pressure, making it manageable for transportation and usage.
Each cylinder undergoes rigorous safety standards to prevent leaks or explosions, making them a reliable resource in scientific experiments like weather balloon launches.
  • Gas cylinders store helium under high pressure (as in the exercise, 100 bar), enabling large quantities to be contained in smaller volumes.
  • Calculating the required number of cylinders involves understanding the pressure and volume relationship of gases, as demonstrated in the exercise using the Ideal Gas Law.
  • This calculation ensures there's enough helium to fully inflate the balloon, allowing it to reach desired altitudes.
Overall, gas cylinders play a pivotal role in transporting and supplying the helium needed to lift weather balloons, exemplifying the practical application of theoretical principles like the Ideal Gas Law in real-world scenarios.

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