In principal one could determine absolute entropy for a substance by integrating dq/T from 0K to the temperature of interest. However, I've seen this done using heat capacities, integrating CdT/T from absolute zero to the temperature of interest. Is there some practical reason that heat cannot be directly measured and integrated over a range of temperatures instead of measuring and integrating heat capacities?

  • $\begingroup$ Heat capacity is defined as the energy required to raise the temp of a substance by 1K. You need heat capacity to relate temp and energy else how're you gonna Integrate? (I'm a high school student, a heavy chance that I'm wrong but I don't think so) $\endgroup$ – Avnish Kabaj Jan 15 '18 at 16:02
  • $\begingroup$ I think that Avatar Shiny is on the right track here. By putting the entropy expression in terms of heat capacity we end up with an expression in the form of dx/x that is easy to integrate. $\endgroup$ – David Rosen Jan 16 '18 at 2:28
  • $\begingroup$ It's easy to integrate if C is constant, or a simple function of T. $\endgroup$ – Chester Miller Jan 16 '18 at 3:39
  • $\begingroup$ Yes makes sense to me now that the original dS = dq/T is changed to dS = CdT/T so that it can be easily integrated. $\endgroup$ – David Rosen Jan 16 '18 at 16:52

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