Animated Solution for Chemistry - Chemical Thermodynamics: Heat required to raise the temperature of $1\text{ mole}$ of a substance by $1^{\circ }$ is called

Have you ever wondered why a metal spoon gets incredibly hot when left in a pot of boiling soup, while a wooden spoon barely warms up? This everyday phenomenon is governed by a fundamental property of matter known as heat capacity. In the realm of chemical thermodynamics, understanding how different substances absorb and store heat is crucial.

Let's dive deep into the problem at hand, which asks us to identify the specific term for the heat required to raise the temperature of $1\text{ mole}$ of a substance by $1^{\circ }$. While it might seem like a simple memory-based question, the distinction between the options provided forms the bedrock of thermodynamic calculations.

When you supply heat energy to a substance, its molecules absorb this energy. This absorbed energy translates into increased kinetic energy of the molecules—they start vibrating, rotating, and translating much faster. Macroscopically, we observe this increased microscopic chaos as a rise in temperature.

However, not all substances respond to heat in the same way. Some substances require a massive amount of heat to show even a tiny increase in temperature, while others heat up very quickly with just a little bit of energy. The general term for the amount of heat required to raise the temperature of a given body by $1^{\circ }\text{C}$ (or $1\text{ K}$) is its heat capacity.

Mathematically, if a heat $q$ produces a temperature change $\Delta T$, the heat capacity $C$ is given by:

But there's a catch. Heat capacity is an extensive property, meaning it depends on the amount of substance you have. A bucket of water will have a much larger heat capacity than a small cup of water. To make this property useful for comparing different materials, we need to standardize the amount of substance.

The Gram's Perspective

If we standardize the amount of substance by mass, specifically to one gram, we get what is known as specific heat (or specific heat capacity).

Specific heat is defined as the amount of heat required to raise the temperature of $1\text{ g}$ of a substance by $1^{\circ }\text{C}$. It is an intensive property, meaning it is independent of the total amount of substance present. The formula modifies to:

where $m$ is the mass in grams. If our question had asked about $1\text{ g}$ of a substance, option (a) would have been the correct answer. But as chemists, we often prefer to count particles rather than weigh them.

The Chemist's Choice

Chemical reactions occur between individual atoms and molecules. Therefore, it is often much more convenient to standardize the amount of substance by the number of particles, specifically to one mole ($6.022\times 10^{23}$ particles).

This brings us to the exact definition asked in the question: The amount of heat required to raise the temperature of $1\text{ mole}$ of a substance by $1^{\circ }\text{C}$ is called its molar heat capacity.

We denote molar heat capacity by $C_m$ (or simply $C$ when the context is clear), and its formula is:

where $n$ is the number of moles. Because the question explicitly specifies "$1\text{ mole}$", the correct terminology is undeniably molar heat capacity. This makes option (b) the correct answer.

To be absolutely thorough, let's quickly rule out the other options.

Water equivalent is a concept often used in calorimetry. It is defined as the mass of water that would absorb the same amount of heat as the given body for the same temperature rise. It is a way to express the heat capacity of an entire apparatus (like a calorimeter) in terms of an equivalent mass of water. It is certainly not the heat required for $1\text{ mole}$ of a substance.

Specific gravity, on the other hand, has absolutely nothing to do with heat. It is the ratio of the density of a substance to the density of a reference substance (usually water). It is a measure of relative density, not thermal properties.

In thermodynamics, precision in language is just as important as precision in mathematics. The subtle difference between "one gram" and "one mole" completely changes the physical quantity we are discussing.

By carefully reading the question and identifying the keyword "$1\text{ mole}$", we can confidently conclude that the heat required is the molar heat capacity. Always keep an eye out for these units and standardizations—they are the classic traps set in competitive exams!