Considering the combined gas law, the pressure of the air in the lungs if the gas expands to 175 ml at a body temperature of 37.0 °C is 1.016 atm.
Combined gas law
The combined gas law combines the three gas laws: Boyle's Law, Charles' Law, and Gay-Lussac's Law.
The combined gas law expresses the relationship between the pressure, volume, and absolute temperature of a fixed amount of gas. It states that the ratio of the product of pressure and volume and the absolute temperature of a gas is equal to a constant:
(P×V)÷T=k
Also, the combined gas law relates "before and after" conditions of a gas:
(P₁×V₁)÷T₁= (P₂×V₂)÷T₂
Pressure of the air in the lungs
In this case, you know:
- P₁= 2.95 atm
- V₁= 55.5 mL
- T₁= 12.5 °C= 285.5 K
- P₂= ?
- V₂= 175 mL
- T₂= 37°C= 310 K
Replacing in the combined gas law:
(2.95 atm× 55.5 mL)÷285.5 K= (P₂×175 mL)÷ 310 K
Solving:
[(2.95 atm× 55.5 mL)÷285.5 K] × (310 K÷175 mL)= P₂
1.016 atm= P₂
Finally, the pressure of the air in the lungs if the gas expands to 175 ml at a body temperature of 37.0 °C is 1.016 atm.