Physics is an interesting and thought-provoking subject. Students should not have the habit of rote learning, rather they should study the subject with an open and fresh mind. Students should constantly keep profiling their minds and stay curious while learning the subject of Physics.
The team of experts at has framed the teaching method in a fashion where they keep provoking the young minds to keep making them learn new concepts, to make them stay curious and open their minds towards the world of science.
This particular topic explains one such concept of Physics for the students. This will help the students have a strong and easy grasp of the topic and also increase their scores in the exams.
The Article Explains The Following Concepts –
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What is Dulong Petit Law?
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Dulong Petit Law Equation
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The Law of Dulong and Petit Formula
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Numerical problem with solution
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Conclusion
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FAQs
What is Dulong Petit Law?
In 1819, two french physicists, Pierre Louis Dulong and Alexis Petit, better known as Dulong and Petit proposed a thermodynamics law, which states the classical expression of Molar specific heat capacity.
According to the Dulong and Petit law, the gram-atomic heat capacity i.e. the product of the specific heat capacity and the atomic mass of an element remains constant. This law was then modified to apply to metallic elements only and now is used to calculate the approximation at intermediately high temperatures.
The modern theory, however built upon the assumption by Einstein in 1907, tells us that the heat capacity of solids is due to the lattice vibrations in the solids. But despite its simplicity, the Dulong and Petit law offers a good prediction for the heat capacity of many elementary solids at higher temperatures.
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Dulong Petit Law Equation
Dulong Petit formula as given by Dulong and Petit, after numerous experiments showed that the heat capacity per weight for several elements was the same. The Dulong Petit derivation is as follows:
The law of Dulong and petit can be mathematically represented as:
[c times M = k ]
Where,
c = specific heat capacity
M = molar mass
k = constant
Dulong and Petit did not know about this constant k. They found that elements with higher atomic weights as given by Dalton and early atomists were smaller and when multiplied by the specific heat capacity, it came out to be a constant. In modern times, this constant came out to be equal to 3R, where R is the gas constant. The Dulong and petit law then became:
[c times M = 3R ]
For a mass m of the sample divided by its molar mass M, gives us the number of moles.
[C times (frac{M}{m}) = 3R ]
[ frac{C}{n} = 3R ]
Where,
C = heat capacity of the element
M = molar mass
m = mass of the sample
n = number of moles
At very low temperatures, the quantum mechanical energy stored within solids manifests itself with a larger and larger effect. The law then fails for substances in the cryogenic region.
The Law of Dulong and Petit Formula
The Dulong and petit law can be used to find the valency and the atomic mass of the elements. The formula given by Dulong and petit is as follows.
[c times M = k ]
Where,
c = specific heat capacity
M = molar mass
k = constant
To find the atomic mass and valency of any element in its solid-state using Dulong petit law equation is given by-
Steps Involved
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Calculate the approximate atomic mass using the formula.
Approx. atomic mass x specific heat capacity = 6.4
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Find the valency of the element using the equation.
Approx. atomic mass = Equivalent mass and valency
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Obtain the nearest whole number for the calculated valency. This is the valency of the element.
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Calculate the corrected atomic mass of the element using:
Corrected atomic mass = Equivalent mass x valency
Limitation of Dulong Petit Law –
Every set of theories comes with its own challenges and limitations. Similarly, the Dulong Petit Law has the following limitations –
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The law is applicable only to those elements which are in solid-state
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The law is not applicable to lighter elements having a high melting point. Thus applicable only to the heavier elements.
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The law gives only an approximate atomic mass. Thus, no exact number is given.
Numerical Problem
The equivalent mass of metal with a specific heat capacity of 0.03 is 69.66. Calculate the valency of the metal and its atomic mass using the law of Dulong and petit formula.
Solution- To find the atomic mass and valency of the metal using Dulong and petit method we will-
Approx. atomic mass x specific heat capacity = 6.4
Approx. atomic mass = [frac{6.4}{0.03} ]
Approx. atomic mass = 213.33
Now that we have obtained the approximate atomic mass, we can calculate the valency of the element using the Dulong law-
Approx. atomic mass = Equivalent mass and valency
[frac{213.33}{69.66} = valency ]
3.06 = valency
By correcting the valency to its nearest whole number we obtain the valency of the element – 3.
Corrected atomic mass = 69.66 x 3
Corrected atomic mass = 208.98
The valency of the metal is 3 and its atomic mass is 208.98u.
Conclusion
The Dulong and petit law gives us an appropriate approximation of specific heat capacity and atomic masses of solids. Certain relationships which Dulong and petit could not explain were later discovered such as the kinetic theory of gasses, which gave the value of the constant they defined as ‘k’. The Dulong petit law stands for metals in their solid-state at higher temperatures
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