If the 1st floor of XXX Hall were at sea level, what would be the difference in

Question

If the 1st floor of XXX Hall were at sea level, what would be the difference in pressure of the air on the 4th floor compared to on the 1st floor (3 stories = 10 meters)? (This is the most challenging question on this set.) (Hint: for a gas, you cannot assume that either volume or density is constant with changes in pressure, but you may assume that air acts as an ideal gas, that its molecular weight is 0.029kg/mol, and that its temperature on the 1st floor is the same as on the 4th floor and is equal to 25

Explanation / Answer

The pressure at the sea level i.e. at the ground level is P0 = 101.3 kpa
The height of the three storie building h = 10 m
The temperature of the air is T = 25+273.15 = 298.15 K

The pressure of the air at the 4 th floor is:

P = P0exp(-mgh/RT)

m is the moleculer mass of the gas = 0.029 kg/mol
g is acceleration due to gravity = 9.8 m/s^2
R is universal gas constant = 8.314 J/mol K

P = (101.3kPa)exp{-(0.029 kg/mol)(9.8 m/s^2)(10 m)/(8.314 J/mol.K)(298.15 K)}
P = 101.1839 kPa
The pressure difference between the ground and fourth floors is DELTA P = P-P0              = 101.3 kPa - 101.1839 kPa              = 0.1161 kPa              = 116.1 Pa

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.