Thermal expansion of a glass rod and a metal ruler

[Brightly]

Homework Statement

A glass rod when measured using a metal scale at 30°C appears to be of length 100 cm. It is known that the scale was calibrated at 0°C, Find true length of the glass rod at (a) 30°C (b) 0°C [Given, coefficient of linear expansion of glass = 8 * 10 ^ (-6) degree C ^ - 1 . coefficient of linear expansion of steel = 26 * 10 ^ (-6) degree C ^ - 1 ]

Relevant Equations

L' = L(1+alpha*del(t))

I can't understand how both the material and the scale's expansion are being taken into account at the respective temperatures. Please explain the concept in detail.

 

[erobz]

Homework Statement: A glass rod when measured using a metal scale at 30°C appears to be of length 100 cm. It is known that the scale was calibrated at 0°C, Find true length of the glass rod at (a) 30°C (b) 0°C [Given, coefficient of linear expansion of glass = 8 * 10 ^ (-6) degree C ^ - 1 . coefficient of linear expansion of steel = 26 * 10 ^ (-6) degree C ^ - 1 ]
Relevant Equations: L' = L(1+alpha*del(t))

I can't understand how both the material and the scale's expansion are being taken into account at the respective temperatures. Please explain the concept in detail.

What they are saying that on the scale a centimeter isn't quite a centimeter at 30 C.

 

[phinds]

@Brightly, you seem to have the mistaken impression that this is a Q&A forum where you just ask the forum to spoon feed you a solution to your problem. It is not.

We are here to help you understand how to solve problems for yourself but it is a requirement that you show some effort on your own first.

Read the forum rules.

 

[Brightly]

I understand your point...but my problem with the question I can't seem to understand the approach to the question, if you can help me that will be very helpful for me.

 

[phinds]

I can't understand how both the material and the scale's expansion are being taken into account at the respective temperatures. Please explain the concept in detail.

Materials change size/shape as temperature changes. You are given the rate at which that change occurs for each of the materials, and you know the temperature that needs to be applied. What is it you don't understand?

 

[Brightly]

Materials change size/shape as temperature changes. You are given the rate at which that change occurs for each of the materials, and you know the temperature that needs to be applied. What is it you don't understand?

I can't understand how to frame the equation for the first statement because I don't quite understand the meaning and also how the equations are being formed as the statements are so interlinked

 

[berkeman]

I can't seem to understand the approach to the question,

Start with the first question, and then go from there. For the first question the ruler measures the glass rod at 30C, but the ruler is calibrated ("correct") at 0C. Given the coefficient of thermal expansion $\alpha$ for steel, how much has the ruler lengthened/expanded at 30C compared to 0C? So that will tell you the length of the glass rod at 30C, right?

 

[berkeman]

I can't understand how to frame the equation for the first statement

Do you see how your Relevant Equation works? It tells you by what fraction the length increases for an increase caused by some temperature difference.

 

[Brightly]

Start with the first question, and then go from there. For the first question the ruler measures the glass rod at 30C, but the ruler is calibrated ("correct") at 0C. Given the coefficient of thermal expansion $\alpha$ for steel, how much has the ruler lengthened/expanded at 30C compared to 0C? So that will tell you the length of the glass rod at 30C, right?

Thank you so much, You cleared all of my doubts. I worked out accordingly and my answer has matched.