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

[roveriscute]

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...

 

[anathema]

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.

 

[ogb p]

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,