Is my understanding of the hot air balloon equation correct?

[Poseidonho]

I had meet a problem when I study the concept of the hot air balloon. The equation was giving
Load = P*V*(1/TempAir - 1/TempBalloon)/R

Then I reverse to

TempBalloon = 1/[1/TempAir -Load*R/(P*V)]

When the volume is less then 1m^3, the temperature calculated giving negative temperature (In kelvin and degree also) but suppose had a greater in temperature with my understanding for the theory.

So is that any wrong in the equation or my understanding?

 

[SteamKing]

In order for the units of your formula to balance correctly, the following quantities must be specified:

Load in kg

Temperatures are in degrees Kelvin

Pressure in Pascals

Volume in cubic meters

R for air is 287.058 J/kg/K

 

[jbriggs444]

So is that any wrong in the equation or my understanding?

As I understand it, you derived an equation that gives the required temperature to give a specified lift, holding everything else (ambient temperature, ambient pressure, volume of the balloon) constant. Now you wonder -- can the equation be correct even though it sometimes gives a negative temperature as a result?

Yes, it can be correct. If the load you are trying to lift is heavier than the mass of the air displaced by the balloon then no matter how hot you heat the air in your balloon, it can never be light enough to have a net upward buoyancy greater than the weight of the load.

The ideal gas law says that a fixed volume with a negative temperature has a negative mass. This is not physically reasonable, but does account for the solution you are getting when the load is too high.

 

[Poseidonho]

Thank You very much, I understand d

 

[PJC01]

I cannot provide a definitive answer without further information. However, based on the given equation and your understanding, it appears that your understanding is incorrect. The hot air balloon equation is based on the ideal gas law, which states that pressure (P), volume (V), and temperature (T) of a gas are directly proportional. The equation you provided is a rearranged version of the ideal gas law, where the load (weight of the balloon and its contents), is factored in.

The equation you have reversed is incorrect because it does not take into account the relationship between pressure, volume, and temperature. It is not possible for the temperature of the balloon to be negative, as this would violate the laws of thermodynamics. Additionally, the equation does not specify the units used for pressure, volume, and temperature, which could also lead to incorrect calculations.

In order to properly understand the concept of the hot air balloon, it is important to understand the ideal gas law and how it applies to the balloon's operation. It is also important to have accurate and complete equations, along with the correct units, to ensure accurate calculations. I recommend consulting with a physics or thermodynamics expert for further clarification and understanding.