It is the balance between thermal energy and intermolecular forces that determines the state of matter of any substance at room temperature. How does thermal energy increase as temperature is doubled?
1) Thermal energy increases by a factor of e (2.718)
2) Thermal energy increases by a factor of R
3)Thermal energy increases by a factor of ten
4)Thermal energy increases by a factor of two

The correct option is;

2) Thermal energy increases by a factor of R

Explanation:

The equipartition energy theorem states that when molecules are in a state of thermal equilibrium, particles within the system posses equal average energy with each degree of freedom which can be known as energy due to a state of having a particular temperature or thermal energy given by the relation

= Kinetic energy of translation + Kinetic energy of rotation + Energy of vibration

For a mono-atomic gas, = 3/2·n·R·T

For a diatomic gas, = 5/2·n·R·T

For a solid element, = 3·n·R·T

Therefore, as the temperature is doubled, the thermal energy increases by a factor of R.