Final answer:
Gamma (heat capacity ratio) is expected to be larger for a gas than for a solid because gas molecules have more degrees of freedom for motion, increasing their heat capacity and therefore increasing the value of gamma.
Step-by-step explanation:
The symbol γ (gamma) represents the heat capacity ratio, which is the ratio of the heat capacity at constant pressure (Cp) to the heat capacity at constant volume (Cv). This ratio is an important variable for describing adiabatic processes for an ideal gas.
Generally, you would expect γ to be larger for a gas than for a solid. In solids, atoms are closely packed together and can only vibrate in place, meaning that the energy added to a solid mainly increases its vibrational kinetic energy.
In contrast, gases have atoms or molecules that are free to move in space, and when energy is added to a gas, it can increase not just the vibrational kinetic energy, but also the translational and sometimes rotational kinetic energy of the molecules.
Since there are more kinds of motion that can be excited in gases, the heat capacity at constant volume (Cv) tends to be larger.
Therefore, since γ is the ratio of Cp to Cv and Cp is always greater than Cv (Cp = Cv + R, where R is the gas constant), γ tends to be higher for gases because they have larger heat capacities due to additional degrees of freedom.