A plastic bag is filled with 1 ft3 of air at 17° C at atmospheric pressure. What is volume at 2 atm pressure?
To find the volume of the plastic bag at 2 atm pressure, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Given:
Initial pressure (P1) = 1 atm
Initial volume (V1) = 1 ft^3
Initial temperature (T1) = 17° C = (17 + 273.15) K (converted to Kelvin)
We are looking for the final volume (V2) at a pressure (P2) of 2 atm.
First, we need to convert the initial temperature to Kelvin:
T1 = 17 + 273.15 = 290.15 K
Now, we can rearrange the ideal gas law equation to solve for V2:
V2 = (P1 * V1 * T2) / (P2 * T1)
Substituting the known values:
V2 = (1 atm * 1 ft^3 * T2) / (2 atm * 290.15 K)
Since the initial volume is given in cubic feet, and the final volume needs to be in the same unit, the units of pressure cancel out, and we are left with:
V2 = (1 ft^3 * T2) / (2 * 290.15 K)
So, to find the volume at 2 atm pressure, you need to multiply the final temperature (in Kelvin) by 1 ft^3 and divide it by (2 * 290.15 K).