A husband buys a helium-filled anniversary balloon for his wife. The balloon has a volume of 4.4 L in the warm store at 74 F. When he takes it outside, where the temperature is 55 F, he finds it has shrunk. By how much has the volume decreased?
To determine the change in volume of the helium-filled balloon when it is taken outside, we need to understand the relationship between temperature and volume. The volume of a gas is directly proportional to its temperature, assuming constant pressure.
The relationship between volume (V) and temperature (T) can be described using the ideal gas law equation: PV = nRT, where P represents pressure, n represents the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
To calculate the change in volume, we need to convert the temperatures from Fahrenheit to Kelvin. The conversion from Fahrenheit to Kelvin is given by the formula: T(K) = (T(°F) - 32) * 5/9 + 273.15.
Given:
Initial volume (V1) = 4.4 L
Initial temperature in Fahrenheit (T1) = 74 °F
Final temperature in Fahrenheit (T2) = 55 °F
First, let's convert the temperatures to Kelvin:
T1(K) = (T1(°F) - 32) * 5/9 + 273.15
T1(K) = (74 - 32) * 5/9 + 273.15
T1(K) = 23.33 + 273.15
T1(K) ≈ 296.48 K
T2(K) = (T2(°F) - 32) * 5/9 + 273.15
T2(K) = (55 - 32) * 5/9 + 273.15
T2(K) ≈ 285.93 K
Now, we can calculate the change in volume:
Change in volume = V1 * (T2(K) - T1(K)) / T1(K)
Change in volume = 4.4 * (285.93 - 296.48) / 296.48
Change in volume ≈ -0.403 L
Therefore, the volume of the helium-filled balloon has decreased by approximately 0.403 L when taken outside.