Hot air balloon physics analysis

Lets examine the physics of a hot air balloon using a sample calculation.
The heated air inside the envelope is at roughly the same pressure as the outside air. With this in mind we can calculate the density of the heated air at a given temperature, using the Ideal gas law, as follows:
P = ?RT
Where:
P is the absolute pressure of the gas, in Pa
? is the density of the gas, in kg/m3
R is the gas constant, in Joules/kg.K
T is the absolute temperature of the gas, in Kelvins (K)
Now,
Normal atmospheric pressure is approximately 101,300 Pa
The gas constant for dry air is 287 Joules/kg.K
The air inside the envelope is typically heated to an average temperature of about 100 degrees Celsius, which is 373 K
Substituting the above three values into the Ideal gas law equation and solving for ? we get ? = 0.946 kg/m3. This is the density of the heated air inside the envelope. Compare this to normal (ambient) air density which is approximately 1.2 kg/m3.
Next, for an average size balloon with an envelope volume of 2800 m3 we wish to determine the net upward buoyant force generated by the envelope.
The net buoyant force is defined here as the difference in density between the surrounding air and the heated air, multiplied by the envelope volume. Thus,
FB,net = (1.2 0.946)x2800 = 711 kg (1565 lb)
This is the net buoyant force pushing upwards on the heated air inside the envelope. The hot air balloon components (such as envelope, gondola, burner, fuel tanks, and passengers) can at most weigh 711 kg in order for the buoyant force to be able to completely lift the hot air balloon off the ground.