[Dolphinsiu]

dU = dq + dw = dq - PexdV ----- (1)

Delta H = Delta U + Delta pV ----- (2)

I truly know that pV in equation (1) means mechanical work done by human while p and V in equation (2) means pressure change and volume change of the system (gas particles itself) respectively due to chemical reaction. Am I correct?

But are they all applicable in reversible process?

Pex = P = nRT (when the process is reversible)
Does that means all ideal gases can undergo reversible process?

[Yggdrasil]

dU = dq + dw = dq - PexdV ----- (1)

Delta H = Delta U + Delta pV ----- (2)

I truly know that pV in equation (1) means mechanical work done by human while p and V in equation (2) means pressure change and volume change of the system (gas particles itself) respectively due to chemical reaction. Am I correct?

For (1) the mechanical work is not necessarily done by a human.  It could be work done by the gas expanding against the external atmospheric pressure.

But are they all applicable in reversible process?

Pex = P = nRT (when the process is reversible)
Does that means all ideal gases can undergo reversible process?

These equations are applicable for both reversible and irreversible processes (In general, if something applies for irreversible processes it will also apply for reversible processes.  The converse is not necessarily true, however.)  For reversible processes, the system is always at equilibrium which means that the internal pressure of the gas is equal to the external pressure applied by the surroundings.  In mathematical terms (for an ideal gas):

P_ext = P = nRT

Ideal gasses can undergo reversible transformations.  However, transformations involving ideal gasses are not necessarily reversible.

[Dolphinsiu]

Thank you very much!I understand what you have said.