Chemistry - Why is entropy change in an irreversible adiabatic process positive?
The friction they are talking about is viscous friction of the gas itself. This comes into play when the gas is deformed rapidly, and is roughly proportional to the square of the rate of gas deformation.
Regarding entropy, the change is entropy is equal to the integral of dq/T only for a reversible process. In an irreversible process, in addition to this exchange of entropy with the surroundings, there is also entropy generated within the system itself.
I agree that the paragraph is highly confusing. For one thing speaking of "heat" in the context of an adiabatic process requires an explanation as to where the heat is going. Clearly for an ideal gas in an adiabatic container the final temperature of the gas depends only on the total work done on gas, and irreversibility must be tied somehow to a difference in the applied external pressure and the internal pressure of the gas. For a reversible process the two would match each other during the compression. In the irreversible case there is a mismatch and some of the work done by the surroundings goes to waste (the applied pressure exceeds the internal pressure), so in the end less work is done (on the gas) than in the reversible case.
The proof that an irreversible adiabatic process has an associated nonzero entropy change starts from the observation that the terminal states for reversible and irreversible adiabatic processes are not the same (in this case for instance the volume is larger in the irreversible compression). To compute the entropy change for the irreversible adiabatic compression you need to identify a reversible process (of which there are many) between the same terminal states as the irreversible process. Evaluating the reversible process that will take the system between the end points of the irreversible process you find that an entropy change is required, even though no heat is exchanged in the actual irreversible adiabatic process and despite reversible adiabatic processes not generating a change in entropy.