Question

On a chilly 12∘C day, you quickly take a deep breath--all your lungs can hold, 4.0 L. The air warms to your body temperature of 37∘C.
If the air starts at a pressure of 1.0 atm, and you hold the volume of your lungs constant (a good approximation) and the number of molecules in your lungs stays constant as well (also a good approximation), what is the increase in pressure inside your lungs?

Answer 1

Answer:

The increase in pressure inside the lungs is 0.09 atm

Explanation:

From the Pressure law

Pressure law states that the volume of a fixed mass of gas is directly proportional to the absolute temperature provided that the volume remains constant.

That is,

P ∝ T

Where P is the Pressure and T is the temperature.

Then, we can write that

P = kT

Where k is the proportionality constant

∴ $\frac{P}{T} = k$

Then,

$\frac{P_{1} }{T_{1} } = \frac{P_{2} }{T_{2} }$

From the question, $P_{1}$ = 1.0 atm

${T_{1}$ = 12 °C = (12 + 273.15) K = 285.15K

${T_{2}$ = 37 °C = (37 + 273.15) K = 310.15K

Therefore,

$\frac{1.0}{285.15} = \frac{P_{2} }{310.15}$

$P_{2} = \frac{1.0 \times 310.15}{285.15}$

$P_{2} = 1.09$ atm

Increase in pressure = $P_{2} - P_{1}$ = 1.09 atm - 1.0 atm

Increase in pressure = 0.09 atm

Hence, the increase in pressure inside the lungs is 0.09 atm