An ideal gas undergoes an adiabatic expansion. Which of the following correctly represents the relat

Question

An ideal gas undergoes an adiabatic expansion. Which of the following correctly represents the relationship between its absolute temperature $T$ and density $\rho$?

Professor PC Thomas Classes · Answer

(a) : For an adiabatic process, the temperature-volume relationship is $TV^{\gamma-1} = 	ext{constant}$. Since density $ho = M/V$, we have $V \propto ho^{-1}$. Substituting this into the adiabatic relation gives $T(ho^{-1})^{\gamma-1} = 	ext{constant}$, which simplifies to $Tho^{1-\gamma} = 	ext{constant}$.