Answer:
The mass of air in kilograms that a person breathes in per day is found toe be 17.352 kg.
Explanation:
The volume intake in the whole day will be given by:
Volume = V = (10 liter/min)(60 min/ 1hr)(24 hr/ 1 day)
V = (14400 liter)(0.001 m^3/ 1 liter)
V = 14.4 m^3/day
Temperture = 20°C = 293 k
Pressure = 1 atm = 101325 N/m²
General gas constant = R = 8.314 J/mol. k
Thus, using general gas equation:
PV = nRT
since, n = m/M
where, n = no. of moles of air
m = mass in grams of air
M = molecular mass of air = 28.97 g/mol
therefore,
PV = (m/M)RT
m = PVM/RT
m = (101325 N/m²)(14.4 m^3/day)(28.97 g/mol)/(8.314 J/mol.k)(293 k)
m = 17352 g/day
m = 17.352 kg/day
The mass of air in kilograms that a person breathes in per day is;
17.3376 kg.
We are given;
Volume of air per minute; v' = 10 L/min = 0.01 m³/min = 14.4 m³/day
Temperature; T = 20°C
Now, formula for density is;
ρ = m/v
where;
ρ is density
m is mass
v is volume
From tables online, the density of air at 20°C air temperature and atmospheric pressure is; ρ = 1.204 kg/m³
From the density equation, we now have;
1.204 = m'/14.4
where m' is the mass of air per day
Thus;
m' = 1.204 × 14.4
m' = 17.3376 kg per day
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