Question

What do you mean by the following statements?
(i) The heat capacity of a body is $50J{K^{ - 1}}$
(ii) The specific heat capacity of copper is $0.4J{g^{ - 1}}{K^{ - 1}}$

Answer 1

Hint: In order to solve a question we need to understand heat. Heat is defined as the energy which flows due to temperature difference. There are three methods of heat flow, conduction, convection and radiation. Conduction states that heat flow is due to exchange of phonons between atoms, this mode of transfer of heat generally occurs in solid, when we heat one side of solid then atoms vibrate and exchange the phonons with neighboring atoms and hence heat conducts.

Complete step by step answer:
Convection is a mode of heat transfer in which matter itself transposes to conduct heat just like hot wind rises up in the atmosphere. Radiation involves exchange of photons to conduct heat transfer.

(i) Heat capacity is defined as the heat transfer per unit change in temperature or it is defined as the amount of energy required by an object to produce a unit change in its temperature. It is an extensive property and is mathematically defined as,
$C = \mathop {\lim }\limits_{\Delta T \to 0} \dfrac{{\Delta Q}}{{\Delta T}}$
So the heat capacity of a body is $50J{K^{ - 1}}$ signifies that $50J$ energy is required by the body to raise its temperature by $1K$.

(ii) Specific heat signifies that amount of energy required by an object of mass $1gm$ to raise its temperature by $1K$. It is mathematically defined as,
$c = \dfrac{{\Delta Q}}{{m\Delta T}}$
So, the specific heat capacity of copper is $0.4J{g^{ - 1}}{K^{ - 1}}$ signifies that $0.4J$ energy is required by body of mass $1gm$ to raise its temperature by $1K$.

Note: It should be remembered that conduction mode and radiation mode does not involve matter exchange in transportation of heat but in conduction heat carried out by matter transposes. In conduction there is a physical contact between the atoms so with exchange of phonon they can conduct heat but in radiation there is no physical contact rather photons are considered to be a ball of energy exchanged to conduct heat.