The formula \(\Delta u = C_{v} \Delta T\)   is valid only for ideal gases undergoing an isochoric process.

Constant-volume specific heat, \(C_v\), is only applicable to isochoric processes.

A 2-kg gas undergoes an isochoric process. If the gas requires 4 kJ of energy to raise its temperature by 1^oC, the gas’s average constant-volume specific heat in this temperature range is 2 kJ/kgK.

A system’s internal energy, \(U\), is a state function.

Two kilograms of water has an internal energy of 10 kJ. The water at this state has a specific internal energy of 5 kJ/kg.

If a system undergoes two different processes, the changes in internal energy, \(\Delta U\), in these two processes must be different.

The total energy in a system free of magnetic, electric, and surface tension effects consists of kinetic energy, potential energy, internal energy and enthalpy.