Question

Question: The specific heat of metal M is \[0.25cal/gK\]. Its equivalent weight is 12.What is its correct atomic weight:
(A) \[25.6\]
(B) \[36\]
(C) \[24\]
(D) \[12\]

Answer 1

Hint: Specific heat term related to thermodynamics. In thermodynamics deals with the forms of heat and heat is the form of energy. And how one energy is converted into other forms of energy.

Complete step by step answer:
Specific heat may be defined as the heat required by the body so that the temperature of the body increases by \[{1^o}\], So that its equal to the mass of water one degree. This is known as specific heat.
According to the Dulong and Petit law- The specific heat is inversely proportional to the atomic weight of the body.
Specific heat \[ \propto \] Atomic weight
Specific heat =\[K \times \] Atomic weight
Here K is the constant and value of K is 6.4
So given in numerical- Specific heat=0.25
Equivalent weight =12
We know Specific heat =\[K \times \] Atomic weight
Here K is the constant and value of K is 6.4
Can be written as- Specific heat =\[6.4 \times \] Atomic weight
Atomic weight\[ = 6.4\]/ specific heat
 Atomic weight=6.4/0.25=25.6
Now we know valency= Atomic weight/equivalent weight
Valency=25.6/12=2
Exact atomic weight= valency\[ \times \]equivalent weight=2\[ \times \]12=24
So, the weight of metal is \[24g/mol\]. The correct answer is option “C” .

Note: Different metals having different specific heat capacity.
Different factors affect the specific heat like numbers of atoms present in a molecule and temperature. And temperature plays a very important role in specific heat capacity.
Specific heat capacity is also very helpful in determining the melting point and boiling point of a substance.