How Much Weight Can a Hot Air Balloon Lift Given Specific Conditions?

[dubsinpubs]

If the volume of a balloon is V=416m^3 and the surrounding air is T=13.8 C. The temperature of the air in the balloon is 213 C. What is the max amount of mass, in addition to the mass of the hot air, the balloon can lift? Density of air is of air outside balloon is 1.22 Kg/m^3.

I know I need to use the Ideal Gas Law PV=nRT. Also the pressure exerted on the balloon by the air in the balloon is = to the pressure by the air outside of the balloon. I know to convert C to Kelvin. The only thing related to mass in this prob is density. I am just stuck on where to go w/ this. Any help would be appreciated :)

 

[Gokul43201]

What is the condition that needs to be satisfied for something to float ?

What is the mass of the hot air in the balloon ? Can this not be calculated using the Gas Law, assuming air is 80% N2 and 20% O2, and the pressure is close to 1 atm (by the argument you used) ?

Think about the first question and take it from there...

 

[M98Ranger]

To solve this problem, we can use the Ideal Gas Law equation PV=nRT to find the amount of gas (in moles) inside the balloon. Since we know the volume (V), temperature (T), and number of moles (n) of the hot air inside the balloon, we can rearrange the equation to solve for pressure (P). Once we have the pressure, we can use the density of air outside the balloon to calculate the mass of air inside the balloon.

First, let's convert the temperature from Celsius to Kelvin by adding 273.15. So the temperature inside the balloon is 213 + 273.15 = 486.15 K.

Next, we can plug in the values we know into the Ideal Gas Law equation: PV = nRT

We know the volume (V) is 416 m^3, the temperature (T) is 486.15 K, and the gas constant (R) is 8.314 J/mol·K. We can also assume that the number of moles (n) of the hot air inside the balloon is equal to the number of moles of air outside the balloon.

So we have: (P)(416) = (n)(8.314)(486.15)

Solving for pressure (P), we get: P = (n)(8.314)(486.15) / 416

Now, we can use the density of air outside the balloon (1.22 kg/m^3) to calculate the mass of air inside the balloon. The density of air (ρ) is equal to the mass (m) divided by the volume (V). So we can rearrange the equation to solve for mass (m).

We know the volume (V) is 416 m^3 and the density (ρ) is 1.22 kg/m^3. So we have: m = (1.22)(416) = 507.52 kg

This is the maximum amount of mass the balloon can lift, in addition to the mass of the hot air inside the balloon. Any additional mass added to the balloon would cause it to sink.