The $2010$ Nobel Prize in Physics was awarded for the discovery of graphene, a two-dimensional form of carbon in which the atoms form a two-dimensional crystal-lattice sheet only one atom thick. Predict the molar specific heat of graphene. Give your answer as a multiple of$R$ .

In the microsystem, the potential energy between the bonds is zero, and the kinetic energy of a monatomic gas is translational. If the temperature varies by a certain amount, $∆T$, then the thermal energy for system is given by equation in the form

$\mathrm{\Delta }{E}_{\mathrm{th}}=\frac{i}{2}nR\mathrm{\Delta }T$.

Where $i$is the number of degrees of freedom,$n$is the number of moles and $R$is the constant of universal gas. Due to the transitory kinetic energy of the molecules, graphene has two degrees of freedom and two vibrational degrees of freedom because it is two-dimensional. As a result, in equation, the thermal energy is provided by

$\mathrm{\Delta }{E}_{\mathrm{th}}=\frac{6}{2}nR\mathrm{\Delta }T=3nR\mathrm{\Delta }T.$

The Specific heat is mentioned by

$\mathrm{\Delta }{E}_{\mathrm{th}}=nC\mathrm{\Delta }T.$

The molar specific heat of a Graphene is

$\begin{array}{c}nC\mathrm{\Delta }T=3nR\mathrm{\Delta }T\\ C=3R.\end{array}$