A hot air balloon is filled with hot air and the hot air forces the volume of the balloon to expand until the density of the gas in the balloon is less than the density of the outside air. The volume must be 20% larger than the balloon would be at STP in order for the balloon to float. If you double the temperature inside the balloon will it float?
Of course.
V=nRT/P
density=mass/volume=mass*P/nRT
if you double temp, density goes to 1/2.
To determine if doubling the temperature inside the balloon will make it float, we need to understand the relationship between temperature, volume, density, and buoyancy.
Buoyancy, which determines whether an object floats or sinks in a fluid, depends on the density of the object compared to the density of the fluid. If the object's density is less than the fluid's density, it will float.
For a hot air balloon, the principle of buoyancy is applied. The balloon is filled with hot air, which is less dense than the surrounding outside air at the same pressure (STP - Standard Temperature and Pressure). This causes the balloon to float.
When the balloon is heated, the hot air inside expands, causing the volume to increase. This decrease in density allows the balloon to float because it becomes less dense than the surrounding air.
Now, let's analyze what happens when the temperature inside the balloon is doubled. According to Charles's Law, which states that the volume of a gas is directly proportional to its absolute temperature, if the temperature is doubled, the volume will also double.
If the volume of the balloon doubles, it means the balloon is now 100% larger than it would be at STP, which is more than the required 20% increase for it to float. Therefore, doubling the temperature inside the balloon will make it float.
To summarize, increasing the temperature inside the balloon will result in the hot air expanding, leading to an increase in volume. Since the volume becomes more than 20% larger than at STP, the balloon will float.