Thermodynamics: Internal Energy and Heat Capacity

This lecture discusses the concepts of internal energy and heat capacity in thermodynamics. The instructor begins by reviewing the definitions of work and heat in closed systems, emphasizing that the change in internal energy is the sum of work done and heat transferred. The lecture covers isothermal processes, where internal energy remains constant despite work being done on the system. The instructor introduces the concept of heat capacity, particularly focusing on isochoric processes where volume remains constant, leading to the definition of constant volume heat capacity. The discussion extends to the degrees of freedom in gases, explaining how energy is distributed among translational, rotational, and vibrational modes. The Boltzmann postulate of equipartition of energy is introduced, illustrating how energy is shared across degrees of freedom. The lecture concludes with examples of heat capacities for different types of gases, highlighting the temperature dependence of heat capacity and the activation of degrees of freedom in diatomic and polyatomic molecules.