How Much Coffee Spills From a Heated Beaker?

[owura143]

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

 

[denverdoc]

what are the units of beta?

 

[Dick]

That looks fine to me. What's the answer supposed to be?

 

[owura143]

The unit is 1/ degrees celsius.





i don't know the right answer

 

[Dick]

Ok. Are you sure that isn't a coefficient of linear expansion? Sorry, but I can't check for you right now.

 

[owura143]

water has no coefficient of linera expansion

 

[denverdoc]

that seems wrong, volume or sg changes by a couple of percent over the range mentioned.

 

[denverdoc]

my bad it asks to be reported in cubic meters. I get the same answer.

 

[hage567]

Where did you get your value for beta from?

 

[denverdoc]

Hage, I looked it up as well, was 0.00021 on Wiki iirc.

 

[Dick]

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.

 

[hage567]

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.