A weather balloon if it starts with 10 liters of helium at 0km elevation and a temperature of 20 degrees. it is released and rises up through the atmosphere to an elevation of 12km where the temperature is -60degrees. calculate the volume of the helium at 12km.
(V1/T1) = (V2/T2)
Remember T must be in kelvin.
To calculate the volume of helium at 12km elevation, we can use the ideal gas law, which states:
PV = nRT
where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
In this case, we are given the initial volume (10 liters) and temperature (20 degrees) at 0km elevation. However, we don't have the pressure and number of moles of helium, so we need to solve for these values first.
Step 1: Convert the given temperatures to Kelvin
The ideal gas law requires temperature to be in Kelvin. To convert Celsius to Kelvin, we add 273.15:
T1 = 20 + 273.15 = 293.15 K (temperature at 0km)
T2 = -60 + 273.15 = 213.15 K (temperature at 12km)
Step 2: Determine the pressure at 0km elevation
Since we don't have the pressure directly, we can assume that it remains constant throughout the ascent. So, the pressure at 0km (P1) is the same as the pressure at 12km (P2).
Step 3: Calculate the number of moles of helium at 0km elevation
To find the number of moles (n), we can use the ideal gas equation:
PV = nRT
We know the volume (V) at 0km is 10 liters, the gas constant (R) is 0.0821 L·atm/(K·mol), and the temperature (T) is 293.15 K. We don't know the pressure (P) at 0km, but we can calculate it later.
n = PV / RT
Step 4: Calculate the volume of helium at 12km elevation
Now we can use the ideal gas law again to find the volume (V2) of helium at 12km:
PV = nRT
We know the number of moles (n) from the previous step, the gas constant (R) is still 0.0821 L·atm/(K·mol), and the temperature (T) at 12km is 213.15 K. We know the pressure (P) at 12km is the same as the pressure at 0km, so we substitute these values into the equation and solve for V2.
V2 = nRT / P2
By following these steps and calculating the pressure at 0km, you can find the volume of helium at 12km using the ideal gas law.