If the temperature of glass and water is decreased to 20.0 ∘C, how much water could be added to the glass?
Coefficient of linear expansion for Water: 210*10^-6
Coefficient of linear expansion for Water: 9*10^-6
I've tried everything and tried looking up how to do it as well, but no one has gotten the answer right. Please help!!!
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Answers & Comments
The secret with many physics problems is to look at your units.
Now you have a volume of water in mL
and a temperature in degrees C
So you are considering a VOLUME and yet you tell us the LINEAR expansion with no units.
So you have confused yourself.
Now the linear expansion of something means just that in one direction along a length.
We have a volume so we can't use the linear expansion.
However when I look up the volumetric expansion of water in Wikipedia they give 206 *10^-6/K. at 20 degrees C.
Because the units are /K (per degrees Kelvin) this tell us immediately that this is a fraction change per degree. (A change of one degree Kelvin exactly the same as one degree change C).
So now we have a clue as to how to do the problem.
For example If it was 0.5/K this means the volume will increase by 0.5 (50%) per degree change from 20C.
We will your figure of 210*10^6 / K and assume it is really volumetric expansion.
Let the volume at 20C be V then change in temperature is (100-20) = 80
then change in volume = V*210*10^-6*20 mL
UNITS CHECK we have volume * (1/Degree) *(Degree) leaving just Volume. Checks OK!
so V + change in volume = 440
so V = 440 - change in volume
V = 440 - V*210*10^-6*20
V[1 + 210*10^-6*20 ] = 440
V = 440 / [1 + 210*10^-6*20 ] mL
= 438.16 mL (to 2 dp)
so the amount we can add after the water has cooled is 440 - 438.16 = 1.84 mL
(I guess we must ignore the fact the water would actually be boiling at 100 C!!