Question

The specific heat of a metal is \[0.16\] , it’s approximate atomic weight would be:

Answer 1

Hint: The unknown atomic weight can be approximately determined by using an important thermodynamic law called the Dulong's Petit law which assumes that all solids have nearly the same product of atomic weights and specific heats.

Complete answer:
The specific heat capacity of any solid substance is the amount of heat needed to bring an increment in the temperature of one kilograms of a solid by one unit. Specific heat capacity is an intensive property and therefore remains unaltered by the changes in size, shape or amount of the concerned solid.
The Dulong's Petit law establishes a relationship between the approximate mass of an unknown solid substance and its specific heat capacity. The two scientists believed that the product of approximate mass and specific heat capacity of the substance at a particular temperature is a constant value. Later, the constant was found out to be equal to \[6.4\] .
Therefore the approximate mass of the metal can be determined using the following relation:
\[{\text{specific heat capacity (}}c) \times {\text{ approx At}}{\text{. mass (}}m) = 6.4\]
On inserting the value of the specific heat capacity in the above relation, the mass can be determined by dividing the constant value by the numerical value of the specific heat capacity.
\[{\text{approx At}}{\text{. mass (}}m) = \dfrac{{6.4}}{{0.16}} = 40g\]
Hence, the value of approximate mass of the metal is \[40g\] according to the Dulong's Petit law.

Note:
Specific heat capacity has a fixed value at a particular temperature but changes with change in the temperature, The Dulong's Petit law is useful and accurate only in high or moderate temperature conditions but fails in low temperature conditions.