Energia Interna e Lei de Hooke

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38 2 INTERNAL ENERGY
P2A.4 (a) n = x/l = (90 nm)/(45 nm) = 2.0 therefore ν = n/N = 2.0/200 = 0.01
F = kT
2l
ln(1 + ν
1 − ν
)
= (1.3806 × 10−23 JK−1) × (298.15K)
(2 × 45 × 10−9 m)
× ln(1 + 0.01
1 − 0.01
) = 9.1 × 10−16 N
(b) �e equation to be plotted is F/N = 4.57×10−14 ln [(1 + ν)/(1 − ν)]; this
is shown in Fig. 2.1.
−1.0 −0.5 0.0 0.5 1.0
−2
0
2
ν
10
13
F/
N
Figure 2.1
�e natural logarithm can be expanded using the Taylor series as ln(1 +
ν) ≈ ν + ν2/2! + ν3/3! + ..., which, for ν