Does gas have just two specific heat capacities or more than two? Is the number of specific heat capacities of a gas countable?

No, the number of specific heat capacities of gas is infinite as it depends on the thermodynamic process followed by the gas.

The specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of one mole of that substance by 1 degree Celsius, or 1 Kelvin. It is denoted by C.

Gases are compressible substances. They have two well-known specific heat capacities: one at constant pressure(Cp)(isobaric process - constant pressure) and another at constant volume(Cv)(isochoric process - constant volume). However, gases can have many specific heat capacities depending on the other thermodynamic processes they follow, like adiabatic process, isothermal process, etc.