Use the properties of the exact differential and the defining equations the derived thermodynamic variables as needed to prove the following relationships:
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- Explain why the spontaneity conditions given in the equation 4.3 and 4.4 are in terms of the general derivatives dU and dH and not some partial derivative of U and H with respect to some other state variable.Can non-pV work be obtained from a process for which G=0? Explain.For an isentropic process, what is the approximate change in U if a system consisting of 1.0mole of gas goes from 7.33atm and 3.04L to 1.00atm and 10.0L? Hint: See the previous problem.
- Which of the following functions are exact differentials? a dF=1xdx+1ydy b dF=1ydx+1xdy c dF=2x2y2dx+3x3y3dy d dF=2x2y3dx+2x3y2dy e dF=xndx+yndy,n= any integer f dF=(x3cosy)dx+(x3siny)dyEquation 4.19 says that (UV)S=p If we are considering the variation of U, the change in the change of the internal energy, we can write that as see the previous problem for an analogous argument ((U)V)S=p Show that this is entirely consistent with the first law of thermodynamics.Efficiency is given by equations 3.5, 3.6, and 3.10. Although we deal mostly with ideal gases in the development of thermodynamics, experimentally we are confined to real gases. Which of the definitions of e are strictly applicable to processes involving real gases as well as ideal gases?
- Thermodynamic properties can also be determined for ions. Determine H,S,andG for the following two reactions, which are simply reactions of dissolution: NaHCO3(s)Na+(aq)+HCO3(aq)Na2CO3(s)2Na+(aq)+CO32(aq) Assume standard conditions standard concentration is 1M for ions in aqueous solution, and consult the table of thermodynamic properties in Appendix 2. What similarities and differences are there?Explain why q is a constant for a given system at a specified temperature.Demonstrate IN DETAIL, and justify the Maxwell relations used, in the proof of the following statement:
- Derive ONLYUse the data and formula below to test the validity of the equation (7) for the two binary systems studied.Recall how the entropy change in phase changes is solved using enthalpy change and temperature. Now that you have learned Gibbs free energy, comment on its validity (i.e. explain how the equation is derived).