Question

While hiking through the desert, you find that you are breathing deeply. Each breath you exhale approximately 3.0 g of air. The air you inhale is is at 25 ∘C at 10% relative humidity. When you exhale the air is at 100% relative humidity at a temperature of 36 ∘C. How many grams of water do you lose each breath?

How much water (L) must you drink each hour if your breathing rate is 3.0×10¹ breaths per minute?

Answer 1

Tin = 298 K (25 C) Tout=309 K (36 C)

Moles of air= 3/28 (molecular wt of air=28)

Patm=101325 pa

Ps-> Saturation pressure

Patm=101325 atm-> Atmospheric pressure

For case of inhaling air

Ps= 10% of Patm => Ps=0.1*101325 atm

Applying ideal gas equation

Ps Vin = R * n * T

Vin (inlet volume) = ( 8.314 * (3/28) * (298) )/ (0.1 *101325)

Vin (inlet volume)= 0.0262 m^3

For case of exhaling air

Ps=1 * Patm = 101325 atm

Applying ideal gas equation

Ps Vo = R * n * T

Vo (outlet volume) = ( 8.314 * (3/28) * (309) )/ (1 *101325)

Vo (oulet volume)= 0.0027 m^3

Net volume lost in 1 breathe = (0.0262-0.0027) m^3

Net volume in litres lost = 0.0235 * 0.001 litres

Water to be drank each hour= 3.0 *101 * 0.0235 * 0.001 * 60= 0.4272 L

Answer= 0.4272 L