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?

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

∴

Then,

From the question, = 1.0 atm

= 12 °C = (12 + 273.15) K = 285.15K

= 37 °C = (37 + 273.15) K = 310.15K

Therefore,

atm

Increase in pressure = = 1.09 atm - 1.0 atm

Increase in pressure = 0.09 atm

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

its c i just checked it