A 3 cu ft ballon is filled with air at 90 degrees F. How many cu ft will that same ballon contain one hour after it is taken into an air conditioned room at 70 degrees F?
Is this your School or your School Subject?
http://www.nhcc.edu/
Math and science experts will help you when they see their subject area listed as a school subject.
To find out how many cubic feet the balloon will contain after one hour in the air-conditioned room, we need to consider the temperature change and its effect on the volume of the balloon.
The volume of a gas is directly proportional to its temperature (measured in Kelvin) if the pressure and amount of gas remain constant. So, we need to convert the given temperatures from Fahrenheit to Kelvin.
Given:
Initial temperature (T1) = 90 degrees F
Final temperature (T2) = 70 degrees F
Initial volume (V1) = 3 cubic feet
To convert Fahrenheit to Kelvin, we can use the formula:
T(°K) = (T(°F) + 459.67) * 5/9
Converting the temperatures:
T1(°K) = (90 + 459.67) * 5/9
T1(°K) = 305.37 °K
T2(°K) = (70 + 459.67) * 5/9
T2(°K) = 295.37 °K
Now we need to apply the temperature-volume relationship using the Kelvin temperatures.
The relationship between volume and temperature can be described by Charles's Law:
V1 / T1 = V2 / T2
Where:
V1 = Initial volume
T1 = Initial temperature (in Kelvin)
V2 = Final volume (what we need to find)
T2 = Final temperature (in Kelvin)
Substituting the known values:
3 / 305.37 = V2 / 295.37
To solve for V2, we can cross-multiply:
3 * 295.37 = 305.37 * V2
886.11 = 93508.13 * V2
Next, divide both sides by 93508.13 to isolate V2:
V2 = 886.11 / 93508.13
V2 ≈ 0.0095 cubic feet
Therefore, after one hour in the air-conditioned room at 70 degrees F, the same balloon will contain approximately 0.0095 cubic feet.