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?

lets assume the linear expansion coefficient for sth is (0.0001) kelvin^-1, its (1) meter long and its at (10) kelvin.

now let's calculate its length when its at (20) kelvin in 2 different ways:

first way: L1-1 = 0.0001*1*10

so: Lfinal=1.001

second way:first let's find its length when its at (15)kelvin:

L2-1=0.0001*1*5

so L2=1.0005

and then let's find its length when it goes from (15) kelvin to (20) kelvin:

L3-1.0005=1.0005*0.0001*5

so: Lfinal=1.00010025!

so if the linear expansion equation is true then:

1.00010025=1.0001

the problem is that the equation doesn't spot the difference between the increase of length that is occurred by increase of mass and the increase of length that is occurred by increase of temperature .

for example :we can have 1 meter and 2 meters long pieces of iron both at 0'c.if first piece(1 meter long one)lengthen (a)meters for every 1'c increase ,second piece will lengthen (2a)meters for every 1'c increase.but a 2 meters long piece of iron that is at 100'c won't lengthen (2a)meters for every 1'c increase.

we can fix that error very easily but why they have defined the equation like this when the fixed form aint very complex ?