assignment 2

# assignment 2 - ASSIGNMENT#2/50 Problems 1.12(c,d 2.5 2.6(b...

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1.1 ASSIGNMENT #2 (/50 ) Problems 1.12(c,d); 2.5; 2.6(b); 2.7; 2.14(a,b) 1.12 Heat capacity c . Based on the Dulong-Petit rule, calculate the heat capacity per mole and per gram of solid silver. How does this compare with the experimental value of 0.235 J K -1 g -1 ? d . Based on the Dulong-Petit rule, calculate the heat capacity per mole and per gram of the silicon crystal. How does this compare with the experimental value of 0.71 J K -1 g -1 ? Solution (/10) c. For solid silver, there are 6 degrees of freedom: 3 vibrational KE and 3 elastic PE terms. Its molar mass is, M at = 107.87 g/mol. ( ) 1 1 mol K J 24.9 = = = 1 1 mol K J 315 . 8 2 6 2 6 R m C (2.5/5) c s = C m / M at = (24.9 J K -1 mol -1 )/(107.87 g/mol) = 0.231 J K -1 g -1 (5/5) This is very close to the experimental value. d. For a solid, heat capacity per mole is 3 R . The molar mass of Si is M at = 28.09 g/mol. ( ) 1 1 mol K J 24.9 = = = 1 1 mol K J 315 . 8 2 6 2 6 R m C (2.5/5) c s = C m / M at = (24.9 J K -1 mol -1 )/(28.09 g/mol) = 0.886 J K -1 g -1 (5/5) The experimental value is substantially less and is due to the failure of classical physics. One has to consider the quantum nature of the atomic vibrations and also the distribution of vibrational energy among the atoms. The student is referred to modern physics texts (under heat capacity in the Einstein model and the Debye model of lattice vibrations).

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1.2 ___________________________________________________________________________________ 2.5 TCR and Matthiessen’s rule Determine the temperature coefficient of resistivity of pure iron and of electrotechnical steel (Fe with 4% C), which are used in various electrical machinery, at two temperatures: 0 ° C and 500 ° C. Comment on the similarities and differences in the resistivity versus temperature behavior shown in Figure 2.39 for the two materials. Solution (/10) 0 0.5 1 1.5 –400 0 400 800 1200 Pure Fe Fe + 4%C Temperature ( ° C) Tangent 0.57 400 ° C 0.23 0.11 0.96 0.53 0.85 0.68 1.05 400 ° C 0.4 500 ° C Resistivity ( μ Ω m) Figure 2Q5-1: Resistivity versus temperature for pure iron and 4% C steel. The temperature coefficient of resistivity α o (TCR) is defined as follows: o o T o o T dT d o ρ ρ ρ α at Slope 1 = = where the slope is d ρ /dT at T = T o and ρ o is the resistivity at T = T o .
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