Question

What is the specific heat capacity of a silver atom, if 386 g of Ag has a heat capacity of 91.5 J/°C?

Answer 1

Hint: To solve the question, we need to understand the concept of heat capacity, specific heat capacity, and the relation between them. Heat capacity is defined as the amount of heat required to raise the temperature of 1 mole of a substance by 1 °C. Specific heat capacity is defined as the amount of heat required to raise the temperature of unit mass (like 1 gram) of substance by 1 °C. If the mass is unity heat capacity is called specific heat capacity.

Complete answer:
Specific heat capacity is given by the formula-
\[Q = mc\Delta T - - - - (1)\]
Where,
$m$ is the mass of the substance
$c$ is the specific heat capacity
$Q$ is the quantity of heat absorbed or released
$\Delta T$ is the change in temperature
The S.I unit of specific heat capacity is $JK{g^{ - 1}}{K^{ - 1}}$.
There is a relation between heat capacity and specific heat capacity-
Heat capacity=Specific heat capacity*Mass$ - - - - (2)$
So the S.I unit of heat capacity is $J/K$.
Given in the question we are given-
$m = 386g$ (Mass of the substance)
$C = 91.5J/^\circ C$ (Heat capacity)
We are asked to find specific heat capacity.
Using equation (2),
Specific heat capacity=Heat capacity/Mass
Specific heat capacity(c),
$ = \dfrac{{91.5J/^\circ C}}{{386g}} = 0.237J/g^\circ C$
So we can say that every gram of silver takes 91.5J of energy to raise the temperature by 1°C.

Note:
It is important to note that specific heat capacity is an intensive property i.e. does not depend on the amount of substance contained however heat capacity is an extensive property i.e. depends on the amount of substance contained. The more the amount of the substance, the more the heat capacity.