Linear expansion coefficient of glass

[nslinker]

Given: The linear expansion coefficient of glass is 9 × 10−6 (◦C)−1. An automobile windshield has dimensions of 60 cm by 400 cm. What minimum spacing around the wind-shield is needed to prevent the windshield from breaking if the temperature changes by 150◦F? Answer in units of mm.

I understand I use the equation alpha*Length*delta(t) but it won't pop out the right answer and I think the dimensions are what is throwing me off. Any advice is appreciated!

 

[Doc Al]

Show what you did. I would have chosen the 400 cm dimension to work with, as it will change the most. Did you convert the temp change to degrees C?

 

[nslinker]

I did not change to degrees Celsius. The conversion is (5/9)*(150-32) so my new temp is 65.556. Also, I have to change cm -> mm. so the dimension would be 4000 mm. So, my final equation would be (9e-6)(4000)(65.556) ??

 

[Doc Al]

So, my final equation would be (9e-6)(4000)(65.556) ??

Yes, but don't forget that that's the total increase in that dimension. So what minimum spacing would you need at each end?

 

[nslinker]

My answer from that comes out to be 2.36 but I don't know how to find the minimum spacing piece that you're talking about.

 

[Doc Al]

If the entire glass expands by 2.36, how much space do you have to allow at each end?

 

[nslinker]

the given dimensions + expansion value.

 

[mochi12]

so i don't know if you already figured out your problem... but i just did that exact problem. the error that you made was that the temp that is given is a (delta t). to convert from F to C it is just (delta t)*(5/9)... you don't subtract 32. that should fix it! after that it is just:

delta L = alpha*Lo*delta t and that should be your answer.

 

[Doc Al]

the error that you made was that the temp that is given is a (delta t). to convert from F to C it is just (delta t)*(5/9)... you don't subtract 32.

Good catch! (I wasn't paying attention when the OP did the conversion. )

I did not change to degrees Celsius. The conversion is (5/9)*(150-32) so my new temp is 65.556.

Fix that conversion. You're converting a temperature change, not a temperature.