Documents

Chapter (6)

Description
Final
Categories
Published
of 44
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
  CHAPTER (VI) ENTROPY   1  6.1: Clausius inequality:  2 To demonstrate the validity of the Clausius inequality, consider a system connected to a thermal energy reservoir at a constant thermodynamic temperature of    T  R   (absolute) through a reversible cyclic device (Fig. 6-1). The cyclic device receives heat  δ Q R   from the reservoir and supplies heat  δ Q to the system whose temperature at that part of the boundary is T    (a variable), while producing work   δ W  rev  . The system produces work δ W  sys   as a result of this heat transfer. FIGURE 6-1   Applying the energy balance to the combined system identified by dashed lines yields: δ W  c  = δ Q R   –   dE  c Eliminating δ Q R  from the two relations above yields: We now let the system undergo a cycle while the cyclic device undergoes an integral number of cycles. Then the preceding relation becomes: where  δ W  c  is the total work of the combined system ( δ W  rev   + δ W  sys   ) and dE  c  is the change in the total energy of the combined system. Considering that the cyclic device is a reversible one, we have: 3   It appears that the combined system is exchanging heat with a single thermal energy reservoir while involving (producing or consuming) work W  c during a cycle. On the basis of the Kelvin-Planck statement of the second law, which states that no system can produce a net amount of work while operating in a cycle and exchanging heat with a single thermal energy reservoir  , we reason that W  c  cannot be a work output, and thus it cannot be a positive quantity. Since T  R  is the thermodynamic temperature and thus a positive quantity, we must have: (6-1) which is the Clausius inequality. “This   inequality   is valid for all thermodynamic cycles, reversible or irreversible, including the refrigeration cycles”  .   4
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks