Ideal gas equation and boyle's law

[moeraeleizhaj]

The mass of a hot-air balloon and its occupants is 289 kg (excluding the hot air inside the balloon). The air outside the balloon has a pressure of 1.01 x 105 Pa and a density of 1.29 kg/m3. To lift off, the air inside the balloon is heated. The volume of the heated balloon is 890 m3. The pressure of the heated air remains the same as that of the outside air. To what temperature in Kelvin must the air be heated so that the balloon just lifts off? The molecular mass of air is 29 u.


Hi, can anyone help me with this question please?
I think it has something to do with the the ideal gas equation (PV=nRT)?
and boyle's law. Can anyone help me start this question

 

[alphysicist]

Hi moeraeleizhaj,

The mass of a hot-air balloon and its occupants is 289 kg (excluding the hot air inside the balloon). The air outside the balloon has a pressure of 1.01 x 105 Pa and a density of 1.29 kg/m3. To lift off, the air inside the balloon is heated. The volume of the heated balloon is 890 m3. The pressure of the heated air remains the same as that of the outside air. To what temperature in Kelvin must the air be heated so that the balloon just lifts off? The molecular mass of air is 29 u.


Hi, can anyone help me with this question please?
I think it has something to do with the the ideal gas equation (PV=nRT)?

Yes, you will need the ideal gas law (unless they want you to use something more accurate).

and boyle's law. Can anyone help me start this question

I don't think boyle's law will help much here, since the appropriate volume is given and the pressure is constant. This problem is about the buoyant force due to hot air. What is the formula for the buoyant force, and what does it need to equal for the balloon to just rise? What answer do you get?