Why is $c_p/c_v$ term introduced in adiabatic process? In an adiabatic process we know there is no change in enthalpy or basically enthalpy change is zero. which means any external work done the internal energy does equal opposite work so as to keep $dH=0$. which means in adiabatic process the pressure and temperature have to change. but while deriving the equation for adiabatic process why do we say that $cp=cv+R$ when this can only be true for isobaric process where pressure is constant and also we introduce the term $cp/cv$ being a constant value called adiabatic constant, my question is why do we even use cp value here while clearly in  the adiabatic process pressure is not constant.
Where am I going wrong? Am I wrong here because $cp=cv+R$ is true for all processes but I thought it is only true for isobaric process.
 A: Let me try to clarify a few key points.

*

*$c_p=c_v+R$ is an equality between two state functions (the specific heat depends on the process connected to the heat transfer, but the final quantity is a function f the state). The two specific heats actually correspond to different processes (isobaric and isochoric). It is wrong to think that the equation is valid for a specific process. A more accurate description of the physics underlying the relation is that a change of entropy at constant pressure can be written as the change at constant volume plus an additional term taking care of the variation of the remaining thermodynamic variables. Notice, that, written this way, it is valid only for ideal gases.

*Enthalpy is a state function depending on entropy and pressure (for a closed system). Therefore the variation of enthalpy is zero for an adiabatic and isobaric process. The reason for the appearance of enthalpy in connection with this formula is that
$$
dH=TdS+Vdp
$$
and
$$
dU=TdS-pdV
$$
Therefore, at constant pressure, the enthalpy change is equal to $TdS=Q_{p,rev}$, while at constant volume $TdS=Q_{v,rev}$, where $Q_{p,rev}$ and $Q_{v,rev}$ are the heat exchanged in a reversible transformation at constant pressure and constant volume respectively.

A: “In an adiabatic process we know there is no change in enthalpy or basically enthalpy change is zero.”
This is untrue. Adiabatic compression of a real or ideal gas will increase its enthalpy and temperature. (For an ideal gas, enthalpy is a function of temperature.)
People often think enthalpy is the stored thermal energy and only heat flow can increase thermal energy. Neither are exactly right, although the former is close to true and true for ideal. It’s the second one. (Finally, theres often also the idea that $pv$ only changes from work, never heat, also untrue.)

“which means any external work done the internal energy does equal opposite work so as to keep =0”.
This is untrue for a different reason. Work can be done on the substance or by it, only.
One thing that is true: at constant pressure the enthalpy change equals the energy exchanged with the environment by heat.
