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?

I think it would float because Volume and Temp are directly proportional. You'd be doubling the volume and would end up with 50% more volume. Just want to make sure my answer is right.

I didn't work through it but your logic is not right. When we talk about doubling the temperature, we usually think in terms of C. Remember you must convert that to kelvin and that isn't doubled.

To determine if doubling the temperature inside the balloon would make it float, we can analyze the relationship between temperature and volume using the ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.

Now, let's consider the factors involved in the scenario. The volume of the balloon needs to be 20% larger than it would be at standard temperature and pressure (STP) for it to float. This additional volume is achieved by filling the balloon with hot air, which reduces the density of the gas inside.

When the temperature of the gas inside the balloon is doubled, we can assume the pressure remains constant. As you correctly mentioned, volume and temperature are directly proportional, according to Charles' Law.

Doubling the temperature would result in a doubling of the volume of the gas, assuming all other factors remain constant. However, based on the given condition that the volume must be 20% larger than it would be at STP, doubling the temperature only leads to a 100% increase in volume. This is not enough to meet the required 20% increase for the balloon to float.

Therefore, the answer is no, doubling the temperature inside the balloon will not make it float.