Warm dense plasma is the matter that exists, roughly, in the range of 10,000 to 10,000,000 Kelvin and has solid-like densities, typically between 0.1 and 10 grams per centimeter. Warm dense fluids like hydrogen, helium, and carbon are believed to make up the interiors of many planets, white dwarfs, and other stars in our universe. The existence of warm dense matter (WDM) on Earth, however, is very rare, as it can only be created with high-energy sources like a nuclear explosion. In such an event, theoretical and computational models that accurately predict the response of certain materials are thus very important. Unfortunately, given both the impracticality of producing WDM on Earth and the inherent complexity of the matter itself (partial ionization, non-negligible electron-nuclei interactions, etc.), modeling WDM has proved strenuous and problematic. Despite this difficulty and complexity, advances in Density Functional Theory Molecular Dynamics (DFT-MD) have made such simulations possible. In this thesis, elemental carbon was modeled because of its low atomic number and its relative abundance of experimental data. The Car-Parrinello MD package implemented in the code Quantum ESPRESSO was used to simulate warm dense carbon. Carbon cells were comprised of 24 atoms assigned random positions and were modeled at densities typical of WDM. System temperature was set with the Nosé-Hoover thermostat and by rescaling ionic velocities, and each cell was run at temperatures up to 10,000 Kelvin. Simulation results were plotted, analyzed, and compared to those presented in the literature. Overall, results show pressure divergence that differs substantially with current DFT models of warm dense carbon. This work continues the application of MD simulations to WDM and provides a basis for future research into thermodynamic properties of warm dense plasmas
