Heat capacity as a function of T under 298 K for metals

In summary, the conversation discusses the heat capacity equation for copper as a function of temperature and its applicability for a broader temperature range. It is noted that the equation provided in the Nist Webbook and other sources only covers a range of 298-1358 K, but may still be accurate for temperatures slightly outside of this range. The accuracy of the equation is also questioned due to the lack of uncertainties in the reference and potential impurities in the copper. It is suggested to compare the equation at different points or create a fit for a different data range.
  • #1
Carlos
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1
The heat capacity equation Cp for copper as a function of temperature (Shomate equation) for the solid phase is defined for the range of 298-1358 K in the Nist Webbook and in many books.

http://webbook.nist.gov/cgi/inchi?ID=C7440508&Mask=2#Thermo-Condensed

And I need to calculate the heat needed to raise temperature from 283.15 to 373.15 K. Are there another coefficients for a broader range (maybe from 273 K to 1358 K) or how could I calculate that accurately?
 
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  • #2
A formula that works from 298 K to 1358 K (a range of more than 1000 K) won't be completely wrong just 16 K below that.
If you are worried about the 15 K extrapolation (with an error of the order of 0.1%), you should be even more worried about the lack of uncertainties in the reference. And what about impurities in your copper?

If you look at the actual data source, the formula seems to be some fit to the tabulated values in 100 K intervals. Don't expect too precise results anyway. There is also a value for 200 K, you can compare the interpolation formula at this point, or make your own fit to a different data range.
 
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1. What is heat capacity and how is it measured?

Heat capacity is the amount of heat energy required to raise the temperature of a substance by one degree. It is typically measured in units of joules per Kelvin (J/K) or calories per degree Celsius (cal/°C). Heat capacity can be measured experimentally by measuring the change in temperature of a substance when a known amount of heat is added to it.

2. How does heat capacity vary with temperature for metals?

Heat capacity is known to vary with temperature for most substances, including metals. In general, the heat capacity of metals increases as temperature increases. This is due to the increase in the number of available energy states for the atoms as they vibrate more at higher temperatures.

3. What is the significance of heat capacity as a function of temperature for metals?

The heat capacity of metals as a function of temperature is important for understanding the thermal properties and behavior of metals. It can help predict how a metal will respond to changes in temperature and how much heat energy is required to raise its temperature. This information is crucial in fields such as materials science and engineering, where precise control of temperature is necessary for various processes.

4. How does heat capacity as a function of temperature differ between different metals?

The specific heat capacity of metals can vary significantly between different metals. This is due to factors such as the atomic structure, the number of valence electrons, and the strength of interatomic bonds. In general, metals with higher atomic masses and more complex atomic structures tend to have higher heat capacities as a function of temperature.

5. Is heat capacity as a function of temperature the same for all metals at room temperature (298 K)?

No, the heat capacity as a function of temperature will vary between different metals at room temperature. This is due to the factors mentioned in the previous answer. Some metals, such as aluminum and copper, have relatively high heat capacities at room temperature, while others, such as lead and mercury, have lower heat capacities. The specific heat capacity of a metal can also vary depending on its physical state (solid, liquid, or gas) at a given temperature.

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