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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:

                      ๐›…q_rev - ๐›…w_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:

                        ๐›…E_in - ๐›…E_out = ฮ”E_system
               ๐›…q_in - q_out + ๐›…w_in - ๐›…w_out = ฮ”E_system (control mass)

shouldn't ๐›…w_out be positive?

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    $\begingroup$ If outgoing work is taken as positive, and weโ€™re interested in the system, then the loss of energy from outgoing work corresponds to a negative number, yes? $\endgroup$ 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 ๐›…W_system > 0 and ๐›…W_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. $\endgroup$ 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. $\endgroup$ Commented Nov 18, 2023 at 4:56

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