help in physics!!!?

Question

there are two parts in this:
1. How is the density of a gas affected by an increase or decrease in temperature?
2. Explain in terms of density and Charles’s Law why heating the air allows a hot-air balloon to float.

help would really be appreciated.

Answer 1

Are we to assume a constant pressure for part 1?

At a constant pressure, when a gas is heated it expands. The mass of the gas can be considered constant at any temperature, but the volume will increase with increasing temperature.
Since Density = mass / volume,
When the volume increases while the mass is constant, the overall density of the gas decreases.
The inverse is true for decreasing temperature….the volume is reduced and the density of increased.

Charles’s Law assumes a constant pressure as the temperature of the gas changes (as in the case above).
V1 / T1 = V2 /T2
If the air in the balloon is at a higher temperature than the air outside, then it has a lower density. Since it has a lower density, it displaces a mass of air greater than its own mass and there is a net upward buoyant force. This upward force acting on the balloon allows the balloon to float.


We can also see this effect by looking at the more general ideal gas law,
PV = nRT
For a constant pressure (P) and number of moles (n), as Temperature (T) increases, the volume (V) must also increase. This shows that the gas will expand when its temperature is increased.
For a constant pressure and volume, as temperature increases, n must decrease. This allows the balloon to weight less than the air it is displacing.
R is the ideal gas rate constant (which can have different values depending on the system of units you are using…but for our purposes, its actual value doesn’t matter too much just so long as it is constant).

Answer 2

1. The higher the temperature, the lower the density. The lower the temperature, the higher the density.
2. When you heat the space inside the hot air balloon, its density becomes lower than the surrounding air and becomes lighter, and hence it floats....

Answer 3

pressure*volume=R*temperature
if pressure increases, density decreases...assuming pressure is constant then volume would have to increase. since you didn't increase the amount of gas (mols) and it is occupying a bigger volume, mass/volume=density

i dont know what charles law is but a hot air balloon floats because the temperature increase with a minimum effect on pressure and volume so the density will decrease so that the air is denser. i think it has more to do with bouancy. the amount of air displaced by the balloon wieghs more than the balloon does...therefore it floats. in other words, the pressure on the underside of the balloon due to the air is more than it is on the top...until it stops floating upwards, then it is equal. density of the balloon and air are equal. denser air is closer to earth.