Calculate Temperature & Density of Balloon at 500m: PV = MRT

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In summary, the balloon filled with ambient air at 15 degrees Celsius and atmospheric pressure of 1.013E5 N/m^2 is lifted up to 500 m by a helicopter where the pressure is 950 hPa. Using the ideal gas law, the internal temperature of the balloon is 75.5 degrees Celsius and its internal density is 1.19 kg/m^3.
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ambient air with 15 degree C and atm pressure of 1.013E5 N/m^2. Balloon is filled with ambient air before it was lifted up to 500 m by a helicopter where the pressure is 950 hPa, what will the balloon's internal temperature and its internal mass density?



I try to use PV = MRT and I found that I have two variables and one equation.


I can obtain M/V from P/RT at the surface. However, I found it's hard to get temperature and density from the given data. Thanks for any input...

 
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Hello!

I can help you with this problem. First, let's rearrange the ideal gas law equation PV = MRT to solve for temperature (T). This gives us T = PV/ MR.

Now, we can plug in our given values for pressure (P), gas constant (R), and molar mass (M) of air. We will use the values for standard temperature and pressure (STP) since the balloon was initially filled with ambient air at 15 degrees Celsius and atmospheric pressure.

So, P = 1.013E5 N/m^2, R = 8.31 J/mol K, and M = 0.02897 kg/mol.

This gives us T = (1.013E5 N/m^2)(0.02897 kg/mol) / (8.31 J/mol K) = 348.5 K or 75.5 degrees Celsius.

Now, to find the density (ρ) of the air inside the balloon, we can use the ideal gas law again. Rearranging it to solve for density gives us ρ = PM/RT.

Using the same values for pressure, gas constant, and molar mass, we get ρ = (1.013E5 N/m^2)(0.02897 kg/mol) / (348.5 K)(8.31 J/mol K) = 1.19 kg/m^3.

Therefore, the balloon's internal temperature is 75.5 degrees Celsius and its internal density is 1.19 kg/m^3.

I hope this helps! Let me know if you have any further questions.
 
  • #3


Dear researcher,

Thank you for sharing your question with me. It is indeed a challenging problem to solve with only one equation and two variables. However, there are a few ways we can approach this problem.

One approach would be to use the ideal gas law, which states that PV = nRT, where n is the number of moles of gas. Since we know the ambient air pressure and temperature at the surface, we can calculate the number of moles of air in the balloon using the ideal gas law. From there, we can use the same equation at the higher altitude to calculate the temperature and density of the air inside the balloon.

Another approach would be to use the adiabatic process equation, which states that P1V1^γ = P2V2^γ, where γ is the specific heat ratio of the gas. This equation can be used to calculate the temperature and density at the higher altitude, assuming that the process is adiabatic (no heat exchange with the surrounding environment).

I understand that this may be a difficult problem to solve, but with some careful calculations and assumptions, we should be able to obtain reasonable estimates for the temperature and density of the balloon at 500m. I hope this helps and good luck with your calculations.

Sincerely,
 

1. How do you calculate the temperature and density of a balloon at 500m using the PV = MRT equation?

The PV = MRT equation is commonly used in thermodynamics to calculate the temperature and density of a gas. In this equation, P represents pressure, V represents volume, M represents the molar mass of the gas, R is the gas constant, and T is the temperature in Kelvin. To calculate the temperature and density of a balloon at 500m, you would need to know the pressure, volume, and molar mass of the gas inside the balloon. Once you have those values, you can rearrange the equation to solve for temperature and density.

2. What is the significance of using the PV = MRT equation when calculating the temperature and density of a balloon at 500m?

The PV = MRT equation is derived from the ideal gas law, which describes the behavior of ideal gases. It is a useful tool for scientists and engineers to calculate the properties of gases, including temperature and density. In the case of a balloon at 500m, this equation can help determine the conditions inside the balloon, which can be important for various applications such as weather forecasting or balloon flights.

3. How does the altitude of a balloon at 500m affect its temperature and density?

The altitude of a balloon at 500m can impact its temperature and density because as altitude increases, the atmospheric pressure decreases. This means that the pressure inside the balloon will be higher than the surrounding air, causing the gas molecules to spread out and the density to decrease. Additionally, the decrease in pressure also leads to a decrease in temperature, as described by the PV = MRT equation.

4. What are the limitations of using the PV = MRT equation to calculate the temperature and density of a balloon at 500m?

The PV = MRT equation assumes that the gas inside the balloon is an ideal gas, meaning that it follows certain laws and behaves in a predictable manner. However, real gases may deviate from these ideal conditions, especially at high pressures and low temperatures. Additionally, the equation does not take into account factors such as humidity, which can also affect the properties of the gas inside the balloon.

5. How can the results of calculating the temperature and density of a balloon at 500m be applied in real-world situations?

The calculation of temperature and density of a balloon at 500m can have various real-world applications. For example, knowing the density of the gas inside a weather balloon can provide information about the atmospheric conditions at that altitude. This data can then be used for weather forecasting. Additionally, this calculation can also be useful in aviation and space exploration, as it can help determine the conditions inside a balloon or spacecraft at different altitudes.

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