Estudio de la expansión lineal en distintos materiales y cálculo del coeficiente de dilatación lineal

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∑L0 = 20 cm + 40 cm + 60 cm

∑L0 = 120 cm

∑L02 = (L0)12 + (L0)22 + (L0)32

∑L02 = (20 cm)2 + (40 cm)2 + (60 cm)2

∑L02 = 5600 cm2

∑L0ΔL = (L0ΔL)1 + (L0ΔL)2 + (L0ΔL)3

∑L0ΔL = (20 cm)*(5 * 10 -3 cm) + (40 cm)*(23 * 10 -3 cm) + (60cm)*(45 * 10 -3 cm)

∑L0ΔL = 3.72 cm2

∑ΔL = ΔL 1 + ΔL 2 + ΔL 3

∑ΔL = 5 * 10 -3 cm + 23 * 10 -3 cm + 45 * 10 -3 cm

∑ΔL = 73 * 10 -3 cm

a = (73 * 10 -3 cm)*(5600 cm2) – (120 cm)*(3.72 cm2)

3 * (5600 cm2) – (120 cm)2

a = - 15.667 * 10 -3 cm

b = 3 * (3.72 cm2) – (120 cm)*(73 * 10 -3 cm)

3 * (5600 cm2) – (120 cm)2

b = 1 * 10 -3

ΔL/1 = a + b * (L0)1

ΔL/1 = - 15.667 * 10 -3 + (1 * 10 -3) * (20 cm)

ΔL/1 = 4.333 * 10 -3 cm

ΔL/2 = a + b * (L0)2

ΔL/2 = - 15.667 * 10 -3 + (1 * 10 -3) * (40 cm)

ΔL/2 = 24.333 * 10 -3 cm

ΔL/3 = a + b * (L0)3

ΔL/3 = - 15.667 * 10 -3 + (1 * 10 -3) * (60 cm)

ΔL/3 = 44.333 * 10 -3 cm

Para el Bronce

∑L0 = (L0)1 + (L0)2 + (L0)3

∑L0 = 20 cm + 40 cm + 60 cm

∑L0 = 120 cm

∑L02 = (L0)12 + (L0)22 + (L0)32

∑L02 = (20 cm)2 + (40 cm)2 + (60 cm)2

∑L02 = 5600 cm2

∑L0ΔL = (L0ΔL)1 + (L0ΔL)2 + (L0ΔL)3

∑L0ΔL = (20 cm)*(21 * 10 -3 cm) + (40 cm)*(48 * 10 -3 cm) + (60cm)*(72 * 10 -3 cm)

∑L0ΔL = 6.66 cm2

∑ΔL = ΔL 1 + ΔL 2 + ΔL 3

∑ΔL = 21 * 10 -3 cm + 48 * 10 -3 cm + 72 * 10 -3 cm

∑ΔL = 141 * 10 -3 cm

a = (141 * 10 -3 cm)*(5600 cm2) – (120 cm)*(6.66 cm2)

3 * (5600 cm2) – (120 cm)2

a = - 4 * 10 -3 cm

b = 3 * (6.66 cm2) – (120 cm)*(141 * 10 -3 cm)

3 * (5600 cm2) – (120 cm)2

b = 1.275 * 10 -3

ΔL/1 = a + b * (L0)1

ΔL/1 = - 4 * 10 -3 + (1.275 * 10 -3) * (20 cm)

ΔL/1 = 21.5 * 10 -3 cm

ΔL/2 = a + b * (L0)2

ΔL/2 = - 4 * 10 -3 + (1.275 * 10 -3) * (40 cm)

ΔL/2 = 47 * 10 -3 cm

ΔL/3 = a + b * (L0)3

ΔL/3 = - 4 * 10 -3 + (1.275 * 10 -3) * (60 cm)

ΔL/3 = 72.5 * 10 -3 cm

- Cálculo de αexp

αexp = (ΔL/) / (L0) * (ΔT)

αexp. promedio = αexp1 + αexp2 + αexp3

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Para el Hierro

αexp1 = (ΔL/)1 / (L0)1 * (ΔT)1

αexp1 = (4.333 * 10 -3 cm) / (20 cm) * (86 0C – 23 0C)

αexp1 = 3.439 * 10 -6 0C -1

αexp2 = (ΔL/)2 / (L0)2 * (ΔT)2

αexp2 = (24.333 * 10 -3 cm) / (40 cm) * (82.5 0C – 23.5 0C)

αexp2 = 10.311 * 10 -6 0C -1

αexp3 = (ΔL/)3 / (L0)3 * (ΔT)3

αexp3 = (44.333 * 10 -3 cm) / (60 cm) * (83 0C – 24 0C)

αexp3 = 12.523 * 10 -6 0C -1

αexp. promedio = 3.439 * 10 -6 0C -1 + 10.311 * 10 -6 0C -1 + 12.523 * 10 -6 0C -1

3

αexp. promedio = 8.758 * 10 -6 0C -1

Para el Bronce

αexp1 = (ΔL/)1 / (L0)1 * (ΔT)1

αexp1 = (21.5 * 10 -3 cm) / (20 cm) * (78 0C – 22 0C)

αexp1 = 19.196 * 10 -6 0C -1

αexp2 = (ΔL/)2 / (L0)2 * (ΔT)2

αexp2 = (47 * 10 -3 cm) / (40 cm) * (80 0C – 22 0C)

αexp2 = 20.259 * 10 -6 0C -1

αexp3 = (ΔL/)3 / (L0)3 * (ΔT)3

αexp3 = (72.5 * 10 -3 cm) / (60 cm) * (80 0C – 22.5 0C)

αexp3 = 21.014 * 10 -6 0C -1

αexp. promedio = 19.196 * 10 -6 0C -1 + 20.259 * 10 -6 0C -1 + 21.014 * 10 -6 0C -1

3

αexp. promedio = 20.156 * 10 -6 0C -1

- Cálculo del error

e = αexp – αteo * 100 %

αteo

Para el Hierro

e = 8.758 * 10 -6 - 12 * 10 -6 * 100 %

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