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# The ratio of specific heat capacity to molar heat capacity of a bodyA. is a universal constantB. depends on the mass of the bodyC. depends on the molecular weight of the bodyD. is dimensionless

Last updated date: 06th Sep 2024
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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 $J/molK$. Taking the ratio of their units will help give the answer.

Formula Used:
The units of Specific heat capacity are: $4.2 \times {10^3}J/kgK$
The units of Molar heat capacity are $J/molK$.

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 $J/molK$.If the ratio the units of specific heat capacity to molar heat capacity is taken, then
$\dfrac{{4.2 \times {{10}^3}J/kgK}}{{J/molK}} = 4.2 \times{10^3}.\dfrac{J}{{kgK}}.\dfrac{{molK}}{J} \\ \therefore\dfrac{{4.2 \times {{10}^3}J/kgK}}{{J/molK}} = 4.2 \times {10^3}\dfrac{{mol}}{{kg}}$

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. Therefore, the ratio of specific heat capacity to molar heat capacity of a body depends on the molecular weight of the body.

Hence, option C is the correct answer.

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.For international use, the Calorie is defined as the amount of heat required to raise the temperature of $1g$ of water from ${14.5^ \circ }C$ to ${15.5^ \circ }C$.