Question

How does molar heat differ from specific heat?

Answer 1

Hint:Specific heat capacity is the amount of heat required to raise the temperature of the unit mass of a substance through one degree. Its units are \[cal/{g^ \circ }C\] . Molar heat capacity of a body is the amount of heat required to raise the temperature of 1 mole of a substance through \[1K\]. Its units are \[J/molK\].

Complete answer:
The branch of heat which deals with measurement of heat is called calorimetry. The SI unit of heat is Joule. Calorie is also a unit of heat. Calorie or \[cal\] is actually defined as the amount of heat required to raise the temperature of \[1g\]of water through \[{1^ \circ }C\]. Kilocalorie or \[kcal\] is the amount of heat required to raise the temperature of \[1kg\] of water by\[{1^ \circ }C\]. Relation between Joule and calorie is given by,
\[1cal = 4.2Joule\] \[ \to (1)\]
Specific heat capacity is the amount of heat required to raise the temperature of the unit mass of a substance through one degree. It can be expressed as \[cal/{g^ \circ }C\] or \[kcal/k{g^ \circ }C\]. Therefore, from equation (1), the specific heat capacity can also be expressed as \[4.2 \times {10^3}J/kgK\].
Molar heat capacity of a body or Molar specific heat is the amount of heat required to raise the temperature of 1 mole of a substance through \[1K\]. Its unit is \[J/molK\]. The molar heat is denoted by \[C\]. The molar specific heat is generally used for gases. For the gases, it is defined at constant volume \[{C_v}\] and at constant pressure \[{C_p}\]. It is found that
\[{C_p} - {C_v} = R\]
where, \[R\] is the molar gas constant.

Note: Molar heat capacity of a body is also referred to as Molar specific heat. For the gases, molar specific is defined at constant volume and constant pressure. If the ratio the units of specific heat capacity to molar heat capacity is taken, then
\[\dfrac{{4.2 \times {{10}^3}J/kgK}}{{J/molK}} = 4.2 \times {10^3}.\dfrac{J}{{kgK}}.\dfrac{{molK}}{J} = 4.2 \times {10^3}\dfrac{{mol}}{{kg}}\]
The ratio \[\dfrac{{mol}}{{kg}}\] is known as molality. Molality is a measure of the number of moles of solute present in 1 kg of solvent. It represents the molar concentration of a solution.