Question

The gas used in separating the two uranium isotopes${}^{\mathbf{235}}\mathit{U}$and${}^{\mathbf{238}}\mathit{U}$have the formula$\mathit{U}{\mathit{F}}_{\mathbf{6}}$. If you added heat at equal rates to a mole of$\mathit{U}{\mathit{F}}_{\mathbf{6}}$gas and a mole of${\mathit{H}}_{\mathbf{2}}$gas, which one’s temperature would you expect to rise faster? Explain.

Short answer

The temperature of$H_2$ rises faster than$U{F}_6$ because it has less degree of freedom.

Step-by-step solution

Understanding the degree of freedom

It measures a specific number of ways the particular molecule moves, like rotation, molecules’s vibration, and translation. This quantity describes the state of any system.

Determination of the molecule’s temperature would expect to rise faster

The$U{F}_6$molecule has many more internal degrees of freedom (rotation, vibration) than$H_2$does.

Therefore, more heat is required for a given temperature change in$U{F}_6$ than$H_2$ , because for$U{F}_6$a larger fraction heat added goes into the internal motions of the molecule and less into the translation motion that determines the temperature.

Said another way,$C_v$ the polyatomic molecule$U{F}_6$ is larger than$C_v$ (diatomic molecule), so a given amount of heat flowing into the gas gives a smaller temperature rise in$U{F}_6$ .

Hence, the temperature of $H_2$rises faster thandata-custom-editor="chemistry" $U{F}_6$ because it has less degree of freedom.