Problem 147 - A Complete Resource Book in Chemistry for JEE Main

Question

Heat required to raise the temperature of \(1 \mathrm{~mol}\) of a substance by \(1^{\circ}\) is called (a) specific heat (b) molar heat capacity (c) water equivalent (d) specific gravity

Step-by-Step Solution

Answer

The correct answer is (b) molar heat capacity.

Step 1: Understanding the Problem

We need to determine what the amount of heat required to raise the temperature of 1 mole of a substance by \(1^{\circ}\) is called. We have four options to consider: specific heat, molar heat capacity, water equivalent, and specific gravity.

Step 2: Analyzing the Options

Let's break down each of the options:(a) Specific heat: This is the heat required to raise the temperature of 1 gram of a substance by \(1^{\circ} \text{C}\).(b) Molar heat capacity: This is the heat required to raise the temperature of 1 mole of a substance by \(1^{\circ} \text{C}\).(c) Water equivalent: This is a measure of the thermal capacity of a substance compared to water.(d) Specific gravity: This is the ratio of the density of a substance to the density of a reference substance, typically water.

Step 3: Selecting the Correct Option

From the analysis, the correct term for the amount of heat required to raise the temperature of 1 mole of a substance by \(1^{\circ}\) is the molar heat capacity. This is because it specifically involves moles, as opposed to grams, which defines specific heat.

Key Concepts

Specific Heat

Specific heat is a fundamental concept in thermodynamics that you often encounter in chemistry and physics. It measures how much heat is needed to increase the temperature of a single gram of any given substance by one degree Celsius. This property is especially useful when you need to understand how a substance reacts to thermal energy.

• The specific heat of water is often used as a reference because it has a relatively high value, meaning it takes more energy to increase its temperature.
• Specific heat values differ for each substance, making it unique and crucial for calculations involving heat transfer.

You might see the formula: \[ q = mc\Delta T \]Where:- \(q\) is the heat added,- \(m\) is the mass,- \(c\) is the specific heat capacity,- \(\Delta T\) is the change in temperature.Understanding specific heat helps in choosing materials for cooking pots, thermal insulators, and in various scientific applications where energy calculations are essential.

Water Equivalent

The term 'water equivalent' refers to a concept that is closely related to specific heat. It is used to simplify the thermal capacity calculations of substances by comparing them to an equivalent amount of water, which is a more commonly known benchmark. Essentially, the water equivalent of a substance is the mass of water that would absorb the same amount of heat for the same temperature change.

• Water equivalent provides a way to compare the heat capacity of substances using water as a reference point.
• This is handy because we know water's specific heat capacity quite well, making it easier to gauge the thermal capacity of other materials in relation to water.

The formula to find water equivalent \(W\) is:\[ W = \frac{m \cdot c}{c_w} \]Where:- \(m\) is the mass of the substance,- \(c\) is the specific heat capacity of the substance,- \(c_w\) is the specific heat capacity of water.Utilizing water equivalent can be helpful in experimental settings, especially where water is used as a calibrating substance for calorimeters.

Specific Gravity

Specific gravity is a crucial concept in fields like chemistry, physics, and engineering. It describes the ratio of the density of a substance to the density of a reference substance, usually water at 4°C because water's density is 1 gram per cubic centimeter under those conditions. By comparing a substance's density to water, specific gravity provides a dimensionless number that helps in identifying substances and their concentrations in mixtures.

• This property is utilized extensively in mineralogy to identify minerals.
• It also helps ascertain the purity of substances and materials.

The formula for specific gravity (SG) is:\[ SG = \frac{\text{density of substance}}{\text{density of reference}} \]Specific gravity can be conveniently measured using a hydrometer or by performing simple density calculations. It plays a pivotal role in processes such as buoyancy, determining whether an object will float or sink in a fluid.