Calculating the Energy Needed to Heat Magnesium: A Challenge!

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SUMMARY

The discussion focuses on calculating the energy required to heat 15g of magnesium from 30°C to 300°C using the temperature-dependent molar specific heat capacity formula: c = a + 2bT - cT^-2. The constants for magnesium are provided as a = 25.7, b = 3.13 x 10^-3, and c = 3.27 x 10^5 J/K·mol. Participants suggest using the integral of the specific heat capacity function over the temperature range to accurately determine the energy required, emphasizing the importance of correctly applying the formula.

PREREQUISITES
  • Understanding of specific heat capacity and its temperature dependence
  • Familiarity with integral calculus for calculating energy
  • Knowledge of the properties of magnesium and its molar mass
  • Ability to manipulate scientific notation in calculations
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  • Study the integration of functions to calculate energy in thermodynamic processes
  • Learn about the specific heat capacities of other materials for comparative analysis
  • Explore the implications of temperature dependence in calorimetry
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Chemistry students, thermodynamics enthusiasts, and professionals involved in materials science or thermal analysis will benefit from this discussion.

davidray
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Any help on this quistion would be greatly appreciated. I have no idea ho to answere it, and can't find anything in my nothes or books anywhere.

The temperature-dependent molar specific heat capacity at constant pressure of many substances is given by: c =a+2bT−cT^−2

For magnesium, the numerical values of the constants are: a=25.7, b=3.13x10^-3, c=3.27x10^5

where c has units J/Kxmol

Calculate the energy required to raise the temperature of 15g of Megnesium from 30 C to 300 C.

I have tried using the formula to qenerate a specific heat capacity for each temperature, but just seem to get crazy numbers that don't make any sense!

Thanks for the help!
 
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When S.H is a constant, c, then energy=c x delta T

which looks like what you'd get from integral of c from T1 to T2

So try integral of c from T1 to T2 where c is a function of T.
 

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