The specific heat of a metal is $0.16.$ Its approximate atomic weight would be
- 40
- 16
- 32
- 64
The Correct Option is A
Approach Solution - 1
Approach Solution -2
Ans. The Dulong and Petit law states that an element's gram-atomic heat capacity, or the sum of its specific heat capacity and atomic mass, remains constant. The approximation is currently calculated at intermediately high temperatures using a modified version of this formula that only applies to metallic components. The contemporary hypothesis, which is based on Einstein's 1907 presumption, claims that solids' ability to store heat is caused by vibrations in their lattices. The Dulong and Petit law provides a reliable forecast for the heat capacity of several fundamental solids at higher temperatures, despite its simplicity.
The Dulong-Petit formula was developed after a number of tests revealed that different components had the same heat capacity per weight. The following is the Dulong Petit derivation: The following is a mathematical illustration of the law of Dulong and Petit:
c x M = k
The specific heat capacity is c, M is molar mass, and k is constant. The constant k was unknown to Dulong and Petit. They discovered that elements with greater atomic weights than those predicted by Dalton and other early atomists were smaller and that the specific heat capacity was constant when multiplied by these smaller elements. This constant was discovered to be equal to 3R in more recent periods, where R is the gas constant. After that, the Dulong and Petit Law became:
c x M = 3R
We may calculate the number of moles by dividing the sample's mass (m) by its molar mass (M).
C x M/m = 3R
C/n = 3R
where C is the element's heat capacity. M = molecular mass, M = sample mass, and M = moles. The quantum mechanical energy that is stored in solids presents itself with an increasing influence at very low temperatures. Then, the legislation is invalid for compounds found in the cryogenic range.
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Concepts Used:
Enthalpy change
Enthalpy Change refers to the difference between the heat content of the initial and final state of the reaction. Change in enthalpy can prove to be of great importance to find whether the reaction is exothermic or endothermic.
Formula for change in enthalpy is:-
dH = dU + d(PV)
The above equation can be written in the terms of initial and final states of the system which is defined below:
UF – UI = qP –p(VF – VI)
Or qP = (UF + pVF) – (UI + pVI)
Enthalpy (H) can be written as H= U + PV. Putting the value in the above equation, we obtained:
qP = HF – HI = ∆H
Hence, change in enthalpy ∆H = qP, referred to as the heat consumed at a constant pressure by the system. At constant pressure, we can also write,
∆H = ∆U + p∆V
Standard Enthalpy of Reaction
To specify the standard enthalpy of any reaction, it is calculated when all the components participating in the reaction i.e., the reactants and the products are in their standard form. Therefore the standard enthalpy of reaction is the enthalpy change that occurs in a system when a matter is transformed by a chemical reaction under standard conditions.