Finding coefficient of linear expansion

[imminentfate]

Hi there :)

At 19^{[tex]\circ[/tex]}C, a rod is exactly 20.08 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 285^{[tex]\circ[/tex]}C, where the rod now measures 20.18 cm on the same ruler. What is the coefficient of linear expansion for the material of which the rod is made?

I used the formula for linear expansion
change in L = Lx(coefficient of linear expansion)(change in temperature)

My attempt:

Steel's coefficient of linear expansion as given by my textbook: 11x10^-6

So over the temperature range of 266 degrees (285 - 19), each centimetre would differ by about (266)(11x10^-6) = 0.002926

Multiplying by 20.18 gives 0.059

Taking this away from 20.18 gives: 20.1209

The change in length will now be: 20.12 - 20.08 = 0.04095

Subbing into the expansion formula:

0.04095 = (20.08)(285 - 19)(a)

a = 7.667x10^-6

This is for an assignment, and I just want to see if I'm heading in the right direction

Thanks in advance

 

[vela]

Hi there :)

At 19^{[tex]\circ[/tex]}C, a rod is exactly 20.08 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 285^{[tex]\circ[/tex]}C, where the rod now measures 20.18 cm on the same ruler. What is the coefficient of linear expansion for the material of which the rod is made?

I used the formula for linear expansion
change in L = Lx(coefficient of linear expansion)(change in temperature)

My attempt:

Steel's coefficient of linear expansion as given by my textbook: 11x10^-6

So over the temperature range of 266 degrees (285 - 19), each centimetre would differ by about (266)(11x10^-6) = 0.002926

Multiplying by 20.18 gives 0.059

Looks fine up to here. I don't follow your logic for what you did next.

Taking this away from 20.18 gives: 20.1209

The change in length will now be: 20.12 - 20.08 = 0.04095

Subbing into the expansion formula:

0.04095 = (20.08)(285 - 19)(a)

a = 7.667x10^-6

This is for an assignment, and I just want to see if I'm heading in the right direction

Thanks in advance

 

[rickz02]

I suggest you clearly define first the 0.059 that you get. What is it actually? Once you get it you'll be in the right track.

 

[imminentfate]

I just thought that since 0.059 is the measurement by which the 'real' and 'expanded' measurements differ on the ruler, taking this away from the 'expanded' value (20.18) will give what the rod's true measurement is.

Is this in any way correct?

 

[imminentfate]

I realized what I did wrong, I just submitted my assignment then and got that question right, so thanks for questioning my method and putting me on the right track, much appreciated :)

 

[vela]

Sorry, I was unable to respond more quickly, but I'm glad you figured it out.