How Does Temperature Affect the Expansion of a Rectangular Plate?

[Rblswimmer456]

Homework Statement

A rectangular plate has an area of 76 cm2.
If the temperature increases by 199 ◦C,
calculate the increase in the area. Use
2 × 10−6 (◦C)−1 as an average coefficient of
linear expansion. Ignore terms of second or-
der.
Answer in units of cm2.

Homework Equations

I looked through my physics book and there wasn't really anything about temperature vs area and I looked online but I didn't find much so I thought I could just you use the equation:

delta(L)= (alpha)(initial L)delta(T) and I just replaced L with A..so it read...
delta(A)=(alpha)(initial A)delta(T)...and alpha being the coefficient of linear expansion

The Attempt at a Solution

delta(A)=(2e-6)(76cm²)(199)

..and this was incorrect...any help would be appreciated to point me in the right direction...thank you!

 

[tiny-tim]

Welcome to PF!

Hi Rblswimmer456! Welcome to PF!

(ahve a delta: ∆ and a degree: ° and try using the X² tag just above the Reply box )

… Use
2 × 10−6 (◦C)−1 as an average coefficient of linear expansion.
…
delta(A)=(2e-6)(76cm²)(199)

"linear expansion" means that every length is multiplied by 2 10^-6 per °C …

so an area is multiplied by … ?

 

[Rblswimmer456]

so since its a "rectangular plate" would 2x10^-6 be multiplied by 4 to get the total linear expansion?

 

[tiny-tim]

oops!

oops! just realized my last post was wrong …

(not completely awake yet! :zzz:)

should have been …

"linear expansion" means that every length is increased by 2 10-6 per °C …

so every length is multiplied by 1.000002 per °C

so an area is multiplied by … ?

so since its a "rectangular plate" would 2x10^-6 be multiplied by 4 to get the total linear expansion?

(did you mean "linear" ? )

no, nor the area expansion

if the length was multiplied by 2, then the area would be multiplied by 4

if the length is multiplied by 1.000002, then the area is multiplied by … ?