I am studying about reversible steady-flow work, and the author of the book states that Taking the positive direction of work to be from the system (work output) the energy balance of a steady-flow device undergoing an internally reversible process is:

                      𝛅q_rev - 𝛅w_rev = dh + dke + dpe

But, if work output is taken as positive, please explain why do we use a negative sign to denote the work output in the equation above when it should be positive?

The same question also holds for general conservation of energy principle where:

                        𝛅E_in - 𝛅E_out = ΔE_system
               𝛅q_in - q_out + 𝛅w_in - 𝛅w_out = ΔE_system (control mass)

shouldn't 𝛅w_out be positive?

Thank you.