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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 = Ξ”E_system
               𝛅q_in - q_out + 𝛅w_in - 𝛅w_out = Ξ”E_system (control mass)

shouldn't 𝛅w_out be positive?

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    $\begingroup$ If outgoing work is taken as positive, and we’re interested in the system, then the loss of energy from outgoing work corresponds to a negative number, yes? $\endgroup$
    – Chemomechanics
    Commented Nov 17, 2023 at 6:20
  • $\begingroup$ More on sign conventions of work in thermodynamics. $\endgroup$
    – Qmechanic ♦
    Commented Nov 17, 2023 at 6:51
  • $\begingroup$ @Chemomechanics but the textbook states that the work done "from the system" is taken as positive, doesn't it mean means 𝛅W_system > 0 and 𝛅W_surr < 0. I intuitively understand when the system does work its internal energy decreases, but these phrasings like 'taking work output as positive' and above sign conventions are confusing the heck out of me. Thanks for the answer by the way. $\endgroup$
    – Prajwal Kori
    Commented Nov 17, 2023 at 10:36

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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?

If work is positive (work done by the system on the surroundings) energy is transferred out of the system. Thus the change in energy in the system is negative. The negative sign in the equation assures us that substituting a positive number for $W$ in the equation results in a negative change in the energy of the system.

If work is negative (work done on the system by the surroundings) energy is transferred into the system. Thus the change in energy in the system is positive. The negative sign in the equation assures us that substituting a negative number for $W$ in the equation results in a positive change in the energy of the system.

Hope this helps.

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  • $\begingroup$ Thank you so much for the explanation. I finally understand the sign convention for work. $\endgroup$
    – Prajwal Kori
    Commented Nov 18, 2023 at 4:56

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