The Mysteries of Simple Equalities in Thermodynamics

[An1MuS]

This is an important concept of thermodynamics,that I'm having some trouble understanding.

My question is, when can we use these equalities?

$$\Delta H=C_{p}\Delta T$$

and

$$\Delta U=C_{v}\Delta T$$

For instance, I thought the first one could only be used when the pressure of the system is constant, but I've seen it being used on compression and expansion of gases.

Does anyone know?

Thanks in advance!

By the way, there's this little thing i don't know too. What's the difference between writing

$$\delta f=...$$ and $$df=...$$

meaning both derivative of "f"

 

[djeitnstine]

This is an important concept of thermodynamics,that I'm having some trouble understanding.

My question is, when can we use these equalities?

$$\Delta H=C_{p}\Delta T$$

and

$$\Delta U=C_{v}\Delta T$$

For instance, I thought the first one could only be used when the pressure of the system is constant, but I've seen it being used on compression and expansion of gases.

Does anyone know?

Thanks in advance!

By the way, there's this little thing i don't know too. What's the difference between writing

$$\delta f=...$$ and $$df=...$$

meaning both derivative of "f"

$$\delta f=...$$ is some finite change in the function. such as evaluating f(1) then f(1.1)

$$df=...$$ is an infinitesimal change in the function.

i.e. the limit as this change goes to 0.