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pennymiller
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Of course!
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pennymiller
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In lab you submerge 100 grams of 40 degree celcius nails in 100 grams of 20 degree celcius water. (The specific heat of iron is 0.12 cal/g celcius). Equate the heat gained by the water to the heat lost by the nails and show that the final temperature becomes 31.4 degrees celcius.
My answer is off. Heres what I did:
The heat gained by water = the heat lost by nails
(c)(m_1)(change in water temperature) = (c)(m_2)(change in nail temperature)
(1)(100)(T-20) = (0.12)(100)(40-T)
since the mass is the same...
(1)(T-20) = (0.12)(40-T)
T-20 = 4.8-.12T
1.12T = 24.8 celcius
It is supposed to be T = 31.4
T = 22.14 celcius
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pennymiller
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Imagine a 40,000 km steel pipe that forms a ring to fit snugly all around the circumference of Planet Earth. Suppose that people along its length breathe on it so as to raise its temperature by 1 degree celcius. The pipe gets longer. It is also no longer snug. How high does it stand above ground level? Show that the answer is an astounding 70 m higher! (To simplify, consider only the expansion of its radial distance from the center of Earth, and apply the geometry formula that relates circumference C and radius r, C = 2 pie r.
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AnnArborBuck
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389
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Sylvania
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pennymiller said :
In lab you submerge 100 grams of 40 degree celcius nails in 100 grams of 20 degree celcius water. (The specific heat of iron is 0.12 cal/g celcius). Equate the heat gained by the water to the heat lost by the nails and show that the final temperature becomes 31.4 degrees celcius.
My answer is off. Heres what I did:
The heat gained by water = the heat lost by nails
(c)(m_1)(change in water temperature) = (c)(m_2)(change in nail temperature)
(1)(100)(T-20) = (0.12)(100)(40-T)
since the mass is the same...
(1)(T-20) = (0.12)(40-T)
T-20 = 4.8-.12T
1.12T = 24.8 celcius
It is supposed to be T = 31.4
T = 22.14 celcius
With the values you gave in the problem the answer is indeed 22.14 and not 31.4. I for one don't think that CP is right for iron, but it is close (my book says .108), that still wouldn't put it at 31.4.
Granted, it has been a long time since I have done an energy balance but I must of did about million of these in college and grad school.
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9 out of 10 voices in my head told me to do it.
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pennymiller
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thanks for verifying that one. Any idea about the cicumference question?
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BenS
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84
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Penny, using 13x10^-6 m/mC as the linear thermal expansion coefficient of steel. with a 1C temperature change the length (circumference) increases 520m. r=40,000,520m/(2PI)=6369510m or a radial increase of 83m using 3.14 as the rounded value of PI
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30 gallon reef June 2007
14 gallon BioCube April 2008
46 gallon bowfront underconstruction
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The Crusher
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24
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Toledo, OH
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pennymiller said :
In lab you submerge 100 grams of 40 degree celcius nails in 100 grams of 20 degree celcius water. (The specific heat of iron is 0.12 cal/g celcius). Equate the heat gained by the water to the heat lost by the nails and show that the final temperature becomes 31.4 degrees celcius.
My answer is off. Heres what I did:
The heat gained by water = the heat lost by nails
(c)(m_1)(change in water temperature) = (c)(m_2)(change in nail temperature)
(1)(100)(T-20) = (0.12)(100)(40-T)
since the mass is the same...
(1)(T-20) = (0.12)(40-T)
T-20 = 4.8-.12T
1.12T = 24.8 celcius
It is supposed to be T = 31.4
T = 22.14 celcius
Penny,
Are you sure the numbers above are correct. If the mass was 1000g the answer is close, or if the temperature was alot hotter for the steel. But, for equal masses the steel has a much lower heat capacity than water. Your answer is correct for the numbers given.
Sorry we are not more help.
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