Calculating Coefficient of Linear Expansion for a Rod Using Temperature Change

[aub]

Homework Statement

At 20° C, a rod is exactly 20.05 cm long on a steel ruler. Both the rod and the ruler are placed in an over at 250° C, where the rod now measure 20.11 cm on the same ruler. What is the coefficient of linear expansion for he material of which the rod is made?

Homework Equations

ΔL = αLiΔT
ΔL= change in length
α= coefficient of linear expansion
ΔT= change in temperature

The Attempt at a Solution

i can only think of one way (ΔT[rod]=ΔT[ruler]) in which i need α of the material of the ruler so it wrong. anyone can give me a hint?

 

[tiny-tim]

hi aub!

… in which i need α of the material of the ruler …

yes, you do need α for steel …

since the question specifies steel, i guess they want you to find it in a table, and use it

 

[aub]

hi aub!


yes, you do need α for steel …

since the question specifies steel, i guess they want you to find it in a table, and use it

i found α for steel
but i got stuck with the measurements since the ruler's 1 cm is now bigger
any help?
thanks

 

[tiny-tim]

how much bigger (using α for steel)?

 

[aub]

how much bigger (using α for steel)?

ΔL(steel)= αLiΔT= 11*10^-6*20.05*230= 0.0507 cm

i didnt get your point though..

 

[tiny-tim]

ok, now that tells you how long 20.11 cm really is!

 

[aub]

ok, now that tells you how long 20.11 cm really is!

ΔL = αLiΔT
ΔL= change in length
α= coefficient of linear expansion
ΔT= change in temperature

So ΔL[ruler]= α[steel]LΔT= 11*10^-6*20.11*230=-0.0508783

ΔL[rod]= -ΔL[ruler]+20.11-20.05= 9.1217*10^-3
α[rod]=ΔL[rod]/[L*ΔT]= 1.9*10^-6

right?

 

[tiny-tim]

hi aub!

sorry, that's too difficult to read and check

can you please use the X² icon just above the Reply box (to do the powers)

and also give the formulas you're using first, so that we can see what everything is!

 

[aub]

hi aub!

sorry, that's too difficult to read and check

can you please use the X² icon just above the Reply box (to do the powers)

and also give the formulas you're using first, so that we can see what everything is!

its one formula that I am using and i already did give it (ΔL = α*Li*ΔT)

So ΔL[ruler]= α[steel]LΔT= 11*10^-6*20.11*230=-0.0508783

ΔL[rod]= -ΔL[ruler]+20.11-20.05= 9.1217*10^-3
α[rod]=ΔL[rod]/[L*ΔT]= 1.9*10^-6