Question

Three identical adiabatic containers A, B and C contain helium, neon and oxygen, respectively, at equal pressure. The gases are pushed to half their original volumes.
(a) The final temperatures in the three containers will be the same.
(b) The final pressures in the three containers will be the same.
(c) The pressures of helium and neon will be the same but that of oxygen will be different.
(d) The temperatures of helium and neon will be the same but that of oxygen will be different.

Answer 1

(c) The pressures of helium and neon will be the same but that of oxygen will be different.
(d) The temperatures of helium and neon will be the same but that of oxygen will be different.

Adiabatic process is expressed as
$$\begin{gathered} p{V}^{\gamma }=\mathrm{constant}\mathrm{or} \\ T{V}^{\gamma -1}=\mathrm{constant}, \end{gathered}$$
where $\gamma =\frac{C_p}{C_v}$ is the ratio of molar heat capacities at constant pressure and volume.
We know that $\gamma$ is equal to 1.67 and 1.40 for a monatomic gas and a diatomic gas, respectively. Helium and neon are monatomic gases and oxygen is a diatomic gas. Therefore, changing the state of the gases, i.e. reducing the volume will lead to identical changes in temperature and pressure for helium and neon and that will be different for oxygen.