Question

an inflated helium balloon with a volume of 0.55l at sea level (1.0atm) is allowed to rise to a height of 6.5km, where the pressure is about 0.40atm. assuming that the temperature remains constant, what is the final volume of the balloon? strategy the amount of gas inside the balloon and its temperature remain constant, but both the pressure and the volume change. what gas law do you need?

Answer 1

Using Boyle's Law, the final volume of a helium balloon rising to a height of 6.5 km with the pressure dropping to 0.40 atm and constant temperature is found to be 1.375 liters.

Step-by-step explanation:

To determine the final volume of an inflated helium balloon that rises from sea level (1.0 atm) to a height of 6.5 km (0.40 atm) while assuming constant temperature, we can use Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional when the temperature is held constant (P1V1 = P2V2). As per the question, we have the initial volume V1 = 0.55 L and pressure P1 = 1.0 atm, and the final pressure at 6.5 km altitude P2 = 0.40 atm.

To solve for the final volume V2, we rearrange Boyle's Law as V2 = (P1V1) / P2. Hence, V2 = (1.0 atm * 0.55 L) / 0.40 atm. Calculating this gives us V2 = 1.375 L.

Therefore, the final volume of the balloon at 6.5 km is 1.375 liters.