Question

A dilute gas expands quasi-statically to three times its initial volume. Is the final gas pressure greater for an isothermal or an adiabatic expansion? Does your answer depend on whether the gas is monatomic, diatomic, or polyatomic?

a) Isothermal; Yes
b) Adiabatic; Yes
c) Isothermal; No
d) Adiabatic; No

Answer 1

The final pressure of a dilute gas after quasi-static expansion is higher in an isothermal process compared to an adiabatic process, because adiabatic expansion results in a steeper drop in pressure. This conclusion does not depend on whether the gas is monatomic, diatomic, or polyatomic.

Step-by-step explanation:

When comparing the final pressures of a dilute gas undergoing quasi-static expansion to three times its initial volume, we look at isothermal and adiabatic processes. During an isothermal expansion, the temperature of the gas is kept constant, and according to Boyle's Law (PV=constant), the pressure decreases proportionally to the increase in volume. In an adiabatic expansion, no heat is exchanged with the surroundings and the pressure decreases as well, but the relationship between pressure and volume follows pVγ = constant, where γ (gamma) is the heat capacity ratio (Cp/Cv). Monatomic gases have a γ value of 5/3, diatomic gases have a γ value of 7/5, and polyatomic gases have lower values of γ. Adiabatic processes involve a steeper pressure drop because γ is always greater than 1, which means that for an adiabatic expansion, pressure decreases more compared to an isothermal expansion at the same volume change.