Question

The specific heat of gold is $ 0.129J{g^{ - 1}}{C^ \circ }^{ - 1} $ . What is the molar heat capacity of gold?

Answer 1

Hint: Heat capacity is a thermodynamic quantity that relates the flow of a particular amount of heat inside a system and the extent by which the temperature gets raised. One form of heat capacity can be converted into another by converting simple physical quantities like amounts etc.

Complete answer:
Thermodynamically, the heat changes are always viewed as a consequence of temperature change and temperature changes are considered an impact of heat exchange between the system and surrounding. Heat capacity is one physical attribute that quantifies this relationship between heat and temperature.
The heat capacity is the amount of heat inflow required by a system to make a single degree rise in its temperature. The specific heat capacity measures the amount of substance as its weight in grams and molar heat capacity measures the amount in terms of number of moles.
The specific heat capacity can be transformed into molar heat capacity by taking the mass of gold in terms of its moles with the help of the molar mass of gold.
On multiplying the specific heat capacity by molar mass, we get the molar heat capacity of the metal.
 $ 0.129J{g^{ - 1}}{C^ \circ }^{ - 1} \times 196.97gmo{l^{ - 1}} = 25.4Jmo{l^{ - 1}} $
 $ \Rightarrow $ Thus, the molar heat capacity of gold is $ 25.4Jmo{l^{ - 1}} $ .

Note:
Heat and temperature can also be changed independently as temperature changes are always observed in adiabatic thermodynamic processes and heat flow is observed in isothermal conditions. Heat capacities are usually measured with the help of calorimeters.