Spring 2008 Final

Spring 2008 Final - YOUR NAME HERE May 17, 2008 Chem 120B...

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Unformatted text preview: YOUR NAME HERE May 17, 2008 Chem 120B Final Examination Definitions and Useful Formulas: E = TS pV + i i dN i A = E TS G = E TS + pV H = E + pV 1 /T = ( S/E ) V,N = ( A/N ) T,V S = k B ln W dE = TdS pdV + i i dN i SdT V dp + i N i d i = 0 dG = SdT + V dp + dN p ( ) = exp( E ) /Q = 1 /k B T dE = dw + dq Q = exp( E ) ( E ) = ( ln Q/ ) V,N dS dq/T Q = exp( A ) ( G ) T,p,N ( A ) T,V,N G = i i N i Q = q N /N ! q trans = V/ 3 = h/ 2 mk B T # ways to distribute N indistinguishable objects among M places = M ! / [ N !( M N )!] ln( M ! / [ N !( M N )!]) ln( M N /N !) for N M i = (0) i + k B T ln ( i / ) i = (0) i + k B T ln x i (0) = ( q 2 / 2 R )(1 1 / ) k TST = (1 / 2) (| d/dt |) p ( ) / integraltext A d p ( ) a A + b B = c C + d D for a A + b B c C + d D u ( r ) = qq / ( r ) ( r ) = qe r/ / ( r ) = radicalbig / (4 i i q 2 i ) ln N ! N ln N N Q = ( m/h ) integraltext dx integraltext dv exp[ E ( x,v )] ( x 2 ) = 2 Dt N ! / ( N 1)! = N T b = k B T 2 b x sol / ( H vap /N ) dp/dT = S/ V 1 1. The first part of this exam concerns a metallic substance composed of atoms of type A. Small portions of the solid and liquid forms of this metal are depicted below: For the entirety of this problem, consider the pressure to be fixed at p = 1atm. Let G solid ( T ) be the Gibbs free energy per particle of the pure solid at temperature T . (In later parts of this problem we will consider impurities in the solid phase.) Denote the pure solids enthalpy per particle as H solid ( T ), and the entropy per particle as S solid ( T ). Similarly, let G liq ( T ), H liq ( T ), and S liq ( T ) be the Gibbs free energy per particle, enthalpy per particle, and entropy per particle of the liquid phase at temperature T . Upon cooling the liquid freezes to form a pure solid at temperature T . When it does so, an amount of heat per particle L is liberated....
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Spring 2008 Final - YOUR NAME HERE May 17, 2008 Chem 120B...

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