Question

Before it was launched, a helium-filled balloon had a pressure of 201 kPa at a temperature of 27°C. At an altitude of 15,000 m, the pressure had decreased to 2.5 kPa, and the temperature had dropped to 14°C. The volume of the balloon increased to 59.3 m^3. What is the original volume of the balloon?

a) 33.1 m^3
b) 44.2 m^3
c) 22.1 m^3
d) 66.3 m^3

Answer 1

To find the original volume of the helium-filled balloon, we applied the combined gas law with the provided pressures, temperatures, and final volume, determining that the original volume is 22.1 m^3.

Step-by-step explanation:

The question asks us to determine the original volume of a helium-filled balloon based on changes in its pressure and temperature at a higher altitude using the ideal gas law. Given that the pressure of the balloon dropped from 201 kPa to 2.5 kPa and the temperature dropped from 27°C to 14°C while the volume increased to 59.3 m3, we can calculate the initial volume before the balloon was launched. To find the original volume, we will use the combined gas law, which is PV/T = constant, where P is pressure, V is volume, and T is temperature in Kelvins. Comparing the conditions at ground level and at altitude:

P1 * V1 / (T1+273) = P2 * 59.3 m3 / (T2+273)

Where P1=201 kPa, T1=27°C, P2=2.5 kPa, T2=14°C. Solving for V1, we can determine that the original volume is option (c) 22.1 m3.