Question

Materials expand when heated. Consider a metal rod of length L0 at temperature T0. If the temperature is changed by an amount ΔT, then the rod's length approximately changes by ΔL=αL0ΔT, where α is the thermal expansion coefficient and ΔT is not an extreme temperature change. For steel, α=1.24×10−5∘C−1. (a) A steel rod has length L0=40cm at T0=40∘C. Find its length at T=90∘C. (b) Find its length at T=50∘C if its length at T0=100∘C is 65 cm. (c) Express length L as a function of T if L0=65cm at T0=100∘C.

Answer 1

Answer:

a)L=40.0248 cm

b)L=64.959 cm

c)L=65+0.000806(T-100)

Explanation:

a)

Given that

Lo=40 cm ,at To=40° C

Lets take length of steel will become L at 90° C.

Given that

ΔL=αLoΔT

Now by putting the values

$\Delta L=1.24\times 10^{-5}\times 40\times (90-40)\ cm$

ΔL=0.0248 cm

We know that

ΔL=L-Lo

So

L=ΔL+Lo

L=0.0248 + 40 cm

L=40.0248 cm

b)

Given that

Lo=65 cm ,at To=100° C

Lets take length of steel will become L at 50° C.

ΔL=αLoΔT

$\Delta L=1.24\times 10^{-5}\times 65\times (50-100)\ cm$

ΔL= - 0.0403 cm

L=ΔL+Lo

L= -0.0403 + 65

L=64.959 cm

c)

Given that

Lo=65 cm ,at To=100° C

$\Delta L=1.24\times 10^{-5}\times 65\times (T-100)\ cm$

L-65=0.000806(T-100)

L=65+0.000806(T-100)