An employee at a party store inflates a spherical helium balloon to a diameter of exactly 12 inches.

Question

An employee at a party store inflates a spherical helium balloon to a diameter of exactly 12 inches. While doing so, she notices that the thermostat is set to 72.0 degrees Fahrenheit. She then takes the balloon outside, where the temperature is 40.0 degrees Fahrenheit. How many liters of helium are in the balloon after she has been outside for a while?

Answer 1

Volume of a spherical balloon with a diamter of 12 inches.

12 inches x 2.54 cm / inch = 30.48 cm

Volume of a sphere = 4/3 π r³ and r = 1/2 diamter = 1/2 x 30.48 cm = 15.24 cm

V = 4/3 x 3.14 x 3540 cm³

V = 14,819 cm³ = 14.8 L = initial volume of the balloon

Assuming the pressure remains constant, we can use the relationship between volume (V) and temperature (T), but T must be in Kelvin. ºF = ºC x 1.8 + 32 and ºC = ºF - 32 / 1.8

T1 = 72.0ºF = 22.2 C + 273 = 295.2K

T2 = 40.0 ºF = 4.44ºC + 273 = 277.4K

V1 = 14.8 L

V2 = ?

Volume and temperature relationship is V1/T1 = V2/T2

14.8 L / 295.2K = V2 / 277.4K

V2 = 13.9 L