Calculating Coefficient of Linear Expansion for a Rod Using Temperature Change

AI Thread Summary
The discussion revolves around calculating the coefficient of linear expansion for a rod based on its length change when heated. Initially, the rod measures 20.05 cm at 20°C and expands to 20.11 cm at 250°C. Participants emphasize the need to account for the linear expansion of the steel ruler, which affects the measurements. The formula used is ΔL = αLiΔT, where ΔL is the change in length, α is the coefficient of linear expansion, and ΔT is the temperature change. Ultimately, the calculated coefficient for the rod is approximately 1.9 x 10^-6.
aub
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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?
 
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hi aub! :wink:
aub said:
… 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 :smile:
 
tiny-tim said:
hi aub! :wink:


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 :smile:

i found α for steel
but i got stuck with the measurements since the ruler's 1 cm is now bigger
any help?
thanks
 
how much bigger (using α for steel)? :smile:
 
tiny-tim said:
how much bigger (using α for steel)? :smile:

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

i didnt get your point though..
 
ok, now that tells you how long 20.11 cm really is! :smile:
 
tiny-tim said:
ok, now that tells you how long 20.11 cm really is! :smile:

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?
 
hi aub! :wink:

sorry, that's too difficult to read and check :redface:

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! :smile:
 
tiny-tim said:
hi aub! :wink:

sorry, that's too difficult to read and check :redface:

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! :smile:

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
 

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