For an irreversible and adiabatic expansion, I understood how calculate the entropy change to the system by using hypothetical path(reversible adiabatic process and isobaric process) But, I don't know why the entropy change to the surroundings is zero . In my textbook, 'it is because that heat transfer to the surroundings is zero. ' but I think that the process must be reversible to explain that like above statement.
Entropy is a physical property of a material, analogous to internal energy and enthalpy. Since the initial and final states of the surroundings are the same, its entropy change is zero.
Or, to determine the change in entropy of your surroundings as a result of the adiabatic irreversible process, you must devise a reversible process for the surroundings that takes it from its initial state to its final state. But its initial state and final state are the same. So any reversible process that you apply to the surroundings will give the same value for its entropy change, namely zero.