Scientists can determine the age of ancient objects by a method called radiocarbon dating. The bombardment of the upper atmosphe
re by cosmic rays converts nitrogen to 14C ,a radioactive isotope of carbon, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14C through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of 14C begins to decrease through radioactive decay. Therefore, the level of radioactivity must also decay exponentially. A parchment fragment was discovered that had about 13% as much 14C radioactivity as does plant material on Earth today. Estimate the age of the parchment.
Select the correct answer.
a) t= 16,724 years
b) none of these
c) t= 17,150 years
d) t= 18,373 years
e) t= 16,866 years
f) t= 16,189 years
Select the correct answer.
a) t= 16,724 years
b) none of these
c) t= 17,150 years
d) t= 18,373 years
e) t= 16,866 years
f) t= 16,189 years
1 answer:
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To solve this problem it is necessary to apply the concepts related to heat exchange and Entropy.
The temperature and mass remain constant, therefore the entropy values will be the only ones to change.
Of the three elements given their entropy values are given by
Part A) From thermodynamic theory we know that temperature is inversely proportional to entropy
Energy remains constant
Therefore the order would be
Lowest Temperature= Water
Medium Temperature= Glass
Highest Temperature=Iron
Part B) In the case of Energy the opposite happens because it is proportional to the entropy, then
Temperature is constant
Lowest Energy = Iron
Medium Energy = Glass
Highest Energy = Water
The variation of entropy of a substance is given by
(1)
where
is the heat exchanged in the process
T is the absolute temperature at which the transformation occurs.
The process in the problem is the solidification of the liquid Gallium, which releases an amount of heat equal to:
where m is the mass of the substance and
is the latent heat of fusion of Gallium. Using m=64.0 g, we find
where the negative sign means the Gallium is releasing heat to the environment.
Now we can use equation (1) to find the variation of entropy, but first we need to convert the temperature into Kelvin:
And so the variation of entropy is
and the negative sign means the entropy in the process is decreasing.
where
T is the absolute temperature at which the transformation occurs.
The process in the problem is the solidification of the liquid Gallium, which releases an amount of heat equal to:
where m is the mass of the substance and
where the negative sign means the Gallium is releasing heat to the environment.
Now we can use equation (1) to find the variation of entropy, but first we need to convert the temperature into Kelvin:
And so the variation of entropy is
and the negative sign means the entropy in the process is decreasing.