Question

The molar specific heat capacity of chromium at the room temperature is $24{\text{ J(}}Kmol{)^{ - 1}}$ and its atomic mass is $52g$ what is specific heat capacity of chromium?

Answer 1

Specific heat capacity and molar heat capacity are two different values for a substance or an element. We can define molar heat capacity as the amount of heat energy which is needed or required to raise the temperature of $1$ mol substance by $1^\circ C$ . It's S.I. Unit is given as $J{\left( {mol{\text{ }}K} \right)^{ - 1}}$ and specific heat capacity is the amount of heat required to raise the temperature of $1$ Kg substance by $1^\circ C$ . It's S.I. Unit is given as $J{(gK)^{ - 1}}$ .

Complete Step By Step Answer:
Specific heat capacity (symbol ${C_p}$ ) is the amount of heat absorbed by a substance or a physical measure. Basically, it is the energy that must be added to a unit mass of matter in the form of heat to raise its temperature by one unit. Specific heat is also a strength characteristic of matter. Dense properties are properties of a given substance and do not depend on the number of substances present. Some other examples of dense attributes include density, color, and so on.
Back to our question, as mentioned earlier, the specific heat of a substance depends on the molar heat capacity and molar mass. If we formulate this relationship, it will be:
${C_p} = \dfrac{{{C_P}}}{n}$
Where ${C_p} =$ specific heat capacity
${C_{mol}} =$ Molar heat capacity
n = molar mass
The molar heat capacity of Chromium is $24{\text{ J(}}Kmol{)^{ - 1}}$ and its atomic mass is given as $52g$ .
Put these values in the formula of calculating specific heat capacity:
${C_p} = \dfrac{{24{\text{ J(}}Kmol{)^{ - 1}}}}{{52gmo{l^{ - 1}}}}$
${C_p} = 0.46\;J/{\left( {gK} \right)^{ - 1}}$
Hence, the specific heat capacity of chromium is $0.46\;J/{\left( {gK} \right)^{ - 1}}$ .

Note:
Specific heat capacity and specific heat capacity are two different things. Specific heat capacity is the measure of the amount of heat or energy which is needed or required so that the temperature of one gram of pure substance increases by one degree Celsius; and the heat capacity is the ratio between the heat transferred to the object and its increase in temperature.