The Vanishing Breath Cloud · AI Generator #GEN-F723F694
Physics · thermodynamics
Problem
On a cold winter morning at T=−10°C, you notice that your breath forms a visible cloud that quickly disappears. The water vapor in your exhaled breath condenses into tiny droplets when it cools. Your breath exits your mouth at body temperature (37°C) and mixes with the cold air.
Assume your exhaled breath can be modeled as an ideal gas that expands and cools as it mixes with the surrounding air. When you exhale normally, about V0=0.50L of air at T0=37°C exits your mouth and expands to three times its original volume as it disperses into the cold environment.
What is the final temperature of your breath after this expansion? Assume the expansion occurs quickly enough to be approximately adiabatic, and use γ=1.4 for air.