text: In many cases, it is preferable to use a slightly modified version of the Gouy-Stodola theorem in work form, where  is replaced by some effective temperature. When this is done, it often enlarges the scope of the theorem, and adapts it to be applicable to more systems or situations. For example, the corrections elaborated below are only necessary when the system exchanges heat with more than one reservoir - if it exchanges heat only at the environmental temperature , the simple form above holds true. Additionally, modifications may change the reversible process to which the real process is compared in calculating . 
  The modified theorem then readswhere  is the effective temperature. 
  For a flow process, let  denote the specific entropy (entropy per unit mass) at the inlet, where mass flows in, and  the specific entropy at the outlet, where mass flows out. Similarly, denote the specific enthalpies by  and . The inlet and outlet, in this case, function as initial and final states a process: mass enters the system at an initial state (the inlet, indexed "1"), undergoes some process, and then leaves at a final state (the outlet, indexed "2").
  This process is then compared to a reversible process, with the same initial state, but with a (possibly) different final state. The theoretical specific entropy and enthalpy after this ideal, isentropic process are given by  and , respectively. When the actual process is compared to this theoretical reversible process and  is evaluated, the proper effective temperature is given byIn general,  lies somewhere in between the final temperature in the actual process  and the final temperature in the theoretical reversible process . 
  This equation above can sometimes be simplified. If both the pressure and the specific heat capacity remain constant, then the changes in enthalpy and entropy can be written in terms of the temperatures, andHowever, it is important to note that this version of the theorem doesn't relate the exact values which the original theorem does. Specifically, in comparing the actual process to a reversible one, the modified version allows the final state to be different between the two. This is in contrast to the original version, wherein reversible process is constructed to match so that the final states are the same.