Change in temperature and length problem help

In summary, the lead rod and glass rod have the same length at 20.8 degrees Celsius and the lead rod is heated to 53.4 degrees Celsius. The question is what temperature the glass rod must be heated to in order for them to be the same length. The formula (change in L)/Lo = (alpha)(change in Temperature) is relevant to this problem, but it is unclear how to set the changes in length of the two rods equal to each other. Additionally, the thermal expansion equation for the glass rod is needed but it is unknown. The constants alpha for lead and glass are also mentioned, but it is unclear how to use them to solve for the temperature of the glass rod. The problem can be solved
  • #1
jmb07
27
0
Lead rod and glass rod have same length at 20.8 degrees celcius. The lead rod is heated to 53.4 degrees celcius. At what temperature must the glass be heated so they are the same length?

I know that (change in L)/Lo = (alpha)(change in Temperature)

but I am not sure how to set (change in L of lead) = (change in L of glass) and i don't know what variables to use to solve for T of glass.

Can anyone help me get started on this one. Much appreciated!
 
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  • #2
What is alpha for lead and glass? Can you write a thermal expansion equation for the glass rod?
 
  • #3
they are just some constants...but i don't know how to set these to equations equal to each other to start the problem...
 
  • #4
Why can't you just set them equal?
 

1. What is the relationship between temperature and length?

The relationship between temperature and length is that as temperature increases, the length of a material also increases. This is known as thermal expansion. Similarly, as temperature decreases, the length decreases. This is due to the movement of molecules becoming more active and spreading out when heated, and becoming less active and closer together when cooled.

2. How does thermal expansion affect materials?

Thermal expansion can cause materials to expand or contract, which can result in changes to their shape, size, and structural integrity. This can be a concern for structures, such as bridges or buildings, as well as for everyday objects like pipes and containers.

3. Can all materials expand and contract when exposed to temperature changes?

Yes, all materials have the ability to expand and contract when exposed to temperature changes. However, the degree of expansion or contraction varies depending on the type of material. Some materials, like metals, have a higher coefficient of thermal expansion and will expand or contract more than others.

4. How is thermal expansion measured?

Thermal expansion is typically measured using the coefficient of thermal expansion (CTE), which is a measure of how much a material will expand or contract per degree of temperature change. The CTE is usually expressed in units of length per unit of temperature (e.g. mm/m°C or in/in°F).

5. Is thermal expansion reversible?

Yes, thermal expansion is reversible. When the temperature of a material returns to its original state, the material will also return to its original length. This is why it is important to consider thermal expansion when designing structures or objects that will be exposed to temperature changes.

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