How Much Coffee Spills From a Heated Beaker?

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A student heated a half-liter beaker of coffee from 20°C to 92°C and sought to calculate the volume of coffee that spilled over due to thermal expansion. The coefficient of volume expansion for water was used, but the initial calculations yielded an incorrect result. Participants discussed the appropriate value for the coefficient, noting it varies with temperature and suggesting that an intermediate temperature might yield a more accurate approximation. There was confusion about whether the coefficient provided was for volume or linear expansion, emphasizing the importance of clarity in units. Ultimately, the discussion highlighted the need for precise values and methods in thermal expansion calculations.
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Urgent help need.Please ! Heat question

1. During an all-night cram session, a student heats up a one-half liter (0.50 10-3 m3) glass (Pyrex) beaker of cold coffee. Initially, the temperature is 20°C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to 92°C. The coefficient of volume expansion of coffee is the same as that of water. How much coffee (in cubic meters) has spilled out of the beaker?



Coefficient of volume expansion for water is 207 x 10^-6

I used the equation

delta V = beta x volume x delta T

= 207x10^-6 X 0.5x10^-3 X 72

= 7.452 X 10 ^-6


But the answer is wrong
 
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what are the units of beta?
 
That looks fine to me. What's the answer supposed to be?
 
The unit is 1/ degrees celcius.





i don't know the right answer
 
Ok. Are you sure that isn't a coefficient of linear expansion? Sorry, but I can't check for you right now.
 
water has no coefficient of linera expansion
 
that seems wrong, volume or sg changes by a couple of percent over the range mentioned.
 
Last edited:
my bad it asks to be reported in cubic meters. I get the same answer.
 
Last edited:
Where did you get your value for beta from?
 
  • #10
Hage, I looked it up as well, was 0.00021 on Wiki iirc.
 
  • #11
denverdoc said:
Hage, I looked it up as well, was 0.00021 on Wiki iirc.

I finally got out from under internet blockages as well, and I notice that that is correct at 20 degrees, but it's over 3 times larger at 90 degrees. Perhaps, choosing an intermediate temperature would give you a better approximation.
 
  • #12
Dick said:
I finally got out from under internet blockages as well, and I notice that that is correct at 20 degrees, but it's over 3 times larger at 90 degrees. Perhaps, choosing an intermediate temperature would give you a better approximation.

Yes, I found that too. I was wondering if the value was stated in the text somewhere or if the OP looked it up.
 

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