problem_set_02

# problem_set_02 - What is the error in your estimate 5...

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Chem 110A, F09 Problem Set 2 1. Think about the plots of C V,m in Fig. 3.2 (3.1 in 1 st edition), and make certain you understand the behavior (i.e., the constancy , and the numerical values , of C V,m ) around room temperature (300K) for He and CO. Similarly, think about and try to understand the increase in C V,m for CO 2 and C 2 H 4 at higher temperatures. 2. Calculate the constant-pressure thermal expansivity β and the isothermal compressibility κ of an ideal gas. 3. Study EXAMPLE PROBLEM 3.5, where it is shown for the van der Waals gas that the change in internal energy at constant temperature, Δ U T , is equal to n 2 a ( 1 V i 1 V f ) . Show that this quantity is small compared to the average internal energy itself, U i or U f , i.e., that the change in internal energy, with volume, at constant temperature, is small. 4. Study EXAMPLE PROBLEM 3.7. Plot C P,m (T) vs T over the range 300 – 600K. What is the average value of C P,m (T) ? Use this average value to calculate the heat absorbed upon heating 143.0g of the sample (solid elemental Carbon) from 300 to 600K at constant pressure (1 atm).
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Unformatted text preview: What is the % error in your estimate? 5. Calculate, and analyze (picking typical values of a and b ), the isothermal compressibility κ for a van der Waals gas, over some interesting ranges of T and V m . As one of these “interesting ranges of T and V m ”, consider in particular the ideal gas limit, i.e., V m >> b and RTV m >> a . 6. Express the hard-to-measure quantity ( ∂ U V ) T in terms of the easy-to-measure β , κ , T and P . 7. Calculate the isothermal compressibility κ for a van der Waals gas, and study its behavior as the critical point ( T c =8a/27Rb , V mc =3b and P c =a/27b 2 ) of the gas is approached. 8. Calculate the Joule-Thomson coefficient for the van der Waals gas, and study its behavior in interesting limits, e.g., in the ideal gas limit, near the critical point, etc. 9. Express ( U V ) T in terms of the Joule-Thomson coefficient, μ J − T = ( T P ) H ....
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