- #1

anisotropic

- 59

- 0

**For example, take the following question:**

The heat capacity of a given ideal gas can be expressed as shown below.

*C*= (10 + 0.006

_{P}*T*) J K

^{-1}mol

^{-1}

Calculate the change in entropy when 4 moles of this gas are isobarically heated from 200 K to 300 K.

**Step 1 of the solution (as given by the solutions manual):**

ΔS = ∫

*d*

_{q}_{rev}/

*T*

Where are they getting this equation from? But more importantly, what is it actually saying, conceptually? I haven't done calculus in years, so I am more than rusty when it comes to integration, meaning I don't even understand what "

*d*" means. Thus, I can't just look at the given expression and figure it out for myself. The actual mechanics of working with integrals, I can figure out on my own; the conceptual part, and where equations are being derived from, not so much.

_{qrev}If someone could help me out, it would be appreciated. Note that I am not looking for a solution to the problem given, as I already have that. Rather, I am requesting an explanation as to why the steps that are involved actually work (an explanation of the integration shown above would be a great start).

For the record, the solution ends up converting

*d*

_{q}_{rev}to

*C*, and integrates from there (200 K to 300 K). But again, I don't know what

_{p}dT*d*

_{q}_{rev}signifies to begin with, so I can't really make sense of any further steps. I do know, however, that

*q*signifies heat transfer in other questions, and "rev" signifies that it is a reversible process (i.e. theoretical), while

*T*is obviously temperature.