The zeroth law states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. It leads to the concept of temperature - a property that is the same for all bodies in thermal equilibrium.

At constant volume all the heat supplied goes to increase the internal energy (no work is done). At constant pressure the gas also expands and does external work, so extra heat is needed for the same temperature rise; hence Cp > Cv. The relation (Mayer's relation) is Cp - Cv = R, where R is the universal gas constant.

Cp - Cv = R

Kelvin-Planck statement: it is impossible to construct an engine that, working in a cycle, converts all the heat absorbed from a source completely into work with no other effect. (Equivalently, Clausius statement: heat cannot flow of its own accord from a colder body to a hotter body.)