Zachary R. answered • 03/13/22
Math, Physics, Mechanics, MatSci, and Engineering Tutoring Made Easy!
Hello Ivan!
Let me try and help you out with your problem.
Since this is an ideal gas, we have the ability to use the Ideal Gas Law.
PV = nRT
...where P is the gas pressure, V is the volume in which the gas is contained, n is the number of moles of gas present, R is the universal gas constant, and T is the absolute temperature.
Note that when using the ideal gas law, we need to be really careful that all of our units of each parameter are compatible with each other. If you like to be safe, then I encourage you to convert all units to their base metric form before plugging in numbers.
In this problem we are analyzing two conditions, and trying to find out the difference in the quantity of air between each condition (the difference in "n").
Let's analyze the original condition...
P1 = 740 mmHg = 98658.6 Pa
V1 = 1.45 x 104 m3
R = 8.314 J / molK
T1 = 20 °C = 293 K
P1V1 = n1RT1
(98658.6 Pa) * (1.45 x 104 m3) = n1 * (8.314 J / molK) * (293 K)
n1 = 587,253.1 mol
So, in the original condition, the ideal gas law predicts that there are ~587,000 moles of air in the house.
Now let's analyze the 2nd condition the same way...
P2 = 780 mmHg = 103991 Pa
V2 = 1.45 x 104 m3
R = 8.314 J / molK
T2 = 35 °C = 308 K
P2V2 = n2RT2
(103991 Pa) * (1.45 x 104 m3) = n2 * (8.314 J / molK) * (308 K)
n2 = 588,847.8 mol
Now, to find how much air must be drawn into the house after changing the temperature and pressure, we just need to find the difference in the number of moles...
Δn = n2 - n1
Δn = (588,847.8 mol) - (587,253.1 mol)
Δn = 1,594.7 mol
So, we predict that around 1594 moles of air must have flowed into the house while the temperature and pressure were changing. So this house is not a "closed system", a.k.a. the house is not air-tight.
Hope that helps!
--Zach
