Question

Molar specific heat of hydrogen (H2) is about (5/2) R in the temperature range of abut 250 to 750 K. At lower temperatures, molar sp. heat of hydrogen decrease to the value typical to mono atomic gases (3/2)R. At higher temperatures, it tends to the values (7/2) R. What do you think is happening?

Answer 1

In the temperature range between 250 K to 750 K, the molecules of hydrogen behave like ****- bells and are free to rotate. As a result, there and 5 degrees of freedom associated with the molecules and corresponding molar sp. heat is 5 x 1/2 RT = 5/2 RT.

At very low temperatures (< 70 K), hydrogen molecules have only translational motion. Thus, the vibration and rotational motions of molecule are absent. There are only 3 degrees of freedom of a molecule and consequently, the specific heat of a mole of a gas is 3 x 1/2 RT = 3/2 RT.

At very hight temperatures (>500 K) apart from translational and rotational motions, vibrational motion of the molecules also takes place.

There are now 7 degrees of freedom of a molecule and the molar sp. heat is 7/2 RT.