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  • The second-law efficiency(heat engines): the ratio of the actualthermal efficiency to the maximum possible (reversible) thermal efficiency under the same conditions

$$\eta_{\mathrm{II}}=\frac{\eta_{\mathrm{th}}}{\eta_{\mathrm{th}, \mathrm{rev}}} \quad($$ heat engines $$)$$

  • The second-law efficiency(work-producing devices): the ratio of the usefulwork output and the maximum possible (reversible) work output

$$\eta_{\mathrm{II}}=\frac{W_{u}}{W_{\mathrm{rev}}} \quad($$ work-producing devices $$)$$

  • The second-law efficiency(work-consuming devices): the ratioof the minimum (reversible) work input to the useful work input

$$\eta_{\mathrm{II}}=\frac{W_{\mathrm{rev}}}{W_{u}}$$

  • The second-law efficiency(refrigerators and heat pumps):

$$\eta_{\mathrm{II}}=\frac{\mathrm{COP}}{\mathrm{COP}_{\mathrm{rev}}}$$

  • The second-law efficiency of a system during a process

$$\eta_{\mathrm{II}}=\frac{\text { Exergy recovered }}{\text { Exergy expended }}=1-\frac{\text { Exergy destroyed }}{\text { Exergy expended }}$$

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