Let's analyze the properties of graphite and diamond, two allotropes of carbon, to determine which statements are correct.

Structure and Bonding:

Diamond: Each carbon atom is $s{p}^3$ hybridized, forming a 3D tetrahedral network. All C-C bonds are single bonds (bond order = 1).

Graphite: Each carbon atom is $s{p}^2$ hybridized, forming 2D hexagonal layers. Within a layer, each carbon is bonded to three others. The C-C bond has a partial double bond character due to resonance; the bond order is approximately 1.33. The layers are held together by weak van der Waals forces.

Analysis of Each Statement:

Statement 1: "Graphite has higher thermal conductivity than diamond."

This is incorrect. Diamond is one of the best known thermal conductors. Its rigid 3D covalent network allows efficient phonon (vibration) transfer. Graphite has good thermal conductivity within its layers, but it is generally lower than diamond's overall conductivity.

Statement 2: "Graphite has higher C–C bond order than diamond."

This is correct. As explained, the C-C bond order in graphite is about 1.33, while in diamond it is exactly 1.

Statement 3: "Graphite is harder than diamond."

This is incorrect. Diamond is the hardest known natural material due to its extensive 3D covalent bonding. Graphite is soft and slippery because its layers can easily slide over each other.

Statement 4: "Graphite has higher electrical conductivity than diamond."

This is correct. Diamond is an electrical insulator because all its valence electrons are involved in strong sigma bonds. In graphite, one electron per carbon is delocalized in a pi-bond cloud above and below each layer, allowing it to conduct electricity parallel to the layers.

Final Answer:

The correct statements are: Graphite has a higher C–C bond order than diamond, and Graphite has higher electrical conductivity than diamond.

Related Topics & Formulae:

Hybridization: The mixing of atomic orbitals to form new hybrid orbitals. $s{p}^3$ (tetrahedral), $s{p}^2$ (trigonal planar).

Bond Order: A measure of the number of chemical bonds between a pair of atoms. Calculated as (number of bonding electrons - number of antibonding electrons)/2.

Allotropy: The property of some chemical elements to exist in two or more different forms, in the same physical state.