Solving the Physics Problem: Density of Hot Air

[chessmath]

Hi
Here is the physics problem that I could not figure out:
Hot air balloons float in the air because of the difference in density between cold and hot air. Consider a balloon in which the mass of the pilot basket together with the mass of the balloon fabric and other equipment is m_b. The volume of the hot air inside the balloon is V_1 and the volume of the basket, fabric, and other equipment is V_2. The absolute temperature of the cold air outside the balloon is T_c and its density is rho_c. The absolute temperature of the hot air at the bottom of the balloon is T_h (where T_h > T_ c}). The balloon is open at the bottom, so that the pressure inside and outside the balloon is the same here. Assume that we can treat air as an ideal gas. Use g for the magnitude of the acceleration due to gravity.


What is the density rho_h(density of hot air) of hot air inside the balloon? Assume that this density is uniform throughout the balloon.
Express the density in terms of T_h, T_c, and rho_c(density of cold air)?

well I first said that because P is constant therefore because pv=nRT rho_h=rho_c*(T_h/T_c)

But I have doubt about this answer because we don't know n(number of moles)
So anybody can help me?
Thanks..

 

[vela]

well I first said that because P is constant therefore because pv=nRT, rho_h=rho_c*(T_h/T_c)

According to your formula, because T_h>T_c, the density of hot air greater than the density of cold air.

But I have doubt about this answer because we don't know n(number of moles)
So anybody can help me?
Thanks..

Hint: You can rearrange the ideal gas law to get$$\frac{n}{V} = \frac{P}{RT}$$