{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# PS1 - h ^ W ^ E D d K d ^ ^ ^ ^ d K t z z t t t h d E ^ d D...

This preview shows pages 1–4. Sign up to view the full content.

Department of Chemical Engineering ChE 210A University of California, Santa Barbara Fall 2011 Problem Set No. 1 Due: Monday, 10/03/10 Objective : To become familiar with the thermodynamic entropy, its derivatives, and its connection to microscopic, molecular properties. Helpful reminders: Take heed of these statistical counting formulas and approximations: ways to pick g1839 objects from g1840 , order matters g1842 g3014 g3015 = g1840! (g1840−g1839)! ways to pick g1839 objects from g1840 , order doesn’t matter g1829 g3015 g3014 = g4672 g1840 g1839 g4673 = g1840! g1839!(g1840−g1839)! ways to pick g1839 objects from g1840 , with replacement g1840 g3014 Stirling’s approximation for factorials lng1840! ≈ g1840lng1840−g1840 Also note that the following approximate expression for the combinations formula, valid for large g1839 and g1840 , will often greatly simplify your work (you should be able to derive this): g1840! g1839!(g1840−g1839)! ≈ g4670g1876 g3051 (1−g1876) g2869g2879g3051 g4671 g2879g3015 whereg1876 ≡ g1839 g1840 1. Statistical antics : After you put the finishing touches on your first perfectly-worked problem set, what’s the first thing that you’re looking forward to exploring in Santa Barbara: (1) outdoorsy activities (hiking, biking, etc.), (2) beach, (3) restaurants / nightlife, (4) the arts (concerts, theater, visual arts, etc), (5) shopping, or (6) historic sites. 2. Fundamentals problem (3 points). Simple functional forms are often used to correlate thermodynamic properties. In one set of experiments, it is found that a pure substance obeys the following heat capacity and equation of state relations: g1831/g1840 = g1855g1846+g1857 g2868 g1842 = g1853g1846g2025 g2871

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
where g2025 = g1840/g1848 and g1853 , g1855 , and g1857 g2868 are g1840 -, g1831 -, and g1848 -independent constants. The first of these expressions invokes the so-called constant heat capacity approximation. Find the underlying entropy function g1845(g1831,g1848,g1840) , up to an g1831 -, and g1848 -independent constant. Be sure to consider that g1845 must have proper extensive behavior.
3. Conceptual problem (1 point). In class, we discussed several properties of the entropy function. One of them was that the entropy is extensive, i.e., g1845(g2019g1831,g2019g1848,g2019g1840) = g2019g1845(g1831,g1848,g1840) for a single-component system. Why is this always the case? You may want to proceed show that lnΩ is extensive. A rough way to do this is to consider a large, macroscopic system of ℴ(10 g2870g2871 ) molecules. For conceptual purposes, we will consider this system to be a cube of sugar. You then “scale” the system by copying it g2019 times over into a much larger cube. What can be said about the interfacial interactions between the different copies, relative to the total energy? Write down

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 7

PS1 - h ^ W ^ E D d K d ^ ^ ^ ^ d K t z z t t t h d E ^ d D...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online