Quantity of Heat & Heat Capacity

Edwin Ogie Library

Quantity of Heat and Heat Capacity

Detailed Lesson Note: Understanding heat as energy, heat capacity versus specific heat capacity, and methods of determination.

Introduction: Heat as a Form of Energy

Heat is a form of energy that flows from a hotter object to a cooler one until thermal equilibrium is reached. Unlike temperature, heat depends on the mass and composition of the substance.

In this lesson, we will define heat capacity and specific heat capacity, discuss how they differ, and show how to determine these properties using simple methods.

Heat Capacity

Heat Capacity is the amount of heat required to raise the temperature of an object by 1°C (or 1 K). It is an extensive property and depends on the amount of substance.

Heat Capacity (C) = Heat added (Q) / Temperature change (ΔT)

Its SI unit is Joules per degree Celsius (J/°C) or Joules per Kelvin (J/K).

Specific Heat Capacity

Specific Heat Capacity is the heat capacity per unit mass of a substance. It is an intensive property.

Specific Heat Capacity (c) = Q / (m × ΔT)

Its SI unit is Joules per kilogram per Kelvin (J/(kg·K)).

Heat Capacity vs Specific Heat Capacity

Although both quantities measure the amount of heat needed to change temperature, heat capacity refers to an entire object (and depends on its mass), whereas specific heat capacity is a property of the material itself.

For example, two objects made of the same material may have different heat capacities if their masses differ, but their specific heat capacities will be the same.

Determination by the Method of Mixtures

The method of mixtures is a common technique to determine the specific heat capacity of a substance. In this method, a heated sample is mixed with a known mass of water at a known temperature. By measuring the final equilibrium temperature, the specific heat capacity can be calculated.

The principle behind this method is the conservation of energy; the heat lost by the hot substance is gained by the water.

Determination by the Electrical Method and Newton’s Law of Cooling

Another method for determining heat capacity involves the electrical method, where an electrical heater is used to supply a known amount of energy to a substance, and the resulting temperature change is measured.

Newton’s Law of Cooling can also be applied to study the rate of cooling, which helps in indirectly determining the heat capacity of a substance.

These methods provide practical ways to measure heat capacity in the laboratory.

Summary and Key Concepts

• Heat: A form of energy transferred between systems due to temperature difference.
• Heat Capacity (C): The amount of heat required to raise the temperature of an object by 1°C (or 1 K).
• Specific Heat Capacity (c): The heat capacity per unit mass of a substance.
• Method of Mixtures: A technique to determine specific heat capacity using energy conservation when mixing substances at different temperatures.
• Electrical Method & Newton’s Law of Cooling: Methods used to determine heat capacity by supplying known energy and measuring cooling rates.

Mastery of these concepts is essential for solving numerical problems related to the quantity of heat.

Extended Discussion and Applications

The determination of heat capacity and specific heat capacity is crucial in many fields including material science, engineering, and thermodynamics. Understanding these properties helps in designing heating and cooling systems, evaluating material performance, and conducting energy efficiency analyses.

Applications include:

• Designing thermal systems such as radiators and heat exchangers.
• Determining energy requirements for industrial processes.
• Studying the thermal behavior of materials under different conditions.

10 Worked Examples on Quantity of Heat (Solutions Hidden)

Example 1: Differentiating Heat Capacity and Specific Heat Capacity

Question: A metal block and a wooden block of the same mass are heated. Explain how the heat capacities and specific heat capacities differ.

Solution:

The heat capacity depends on both the material and its mass. Even if the masses are equal, the metal may have a lower specific heat capacity than the wood. Therefore, the metal block requires less heat to raise its temperature by 1°C compared to the wooden block.

Example 2: Using the Method of Mixtures

Question: A 50 g sample of metal at 100°C is placed into 200 g of water at 20°C. The final temperature is 25°C. Describe how to determine the specific heat capacity of the metal.

Solution:

Using conservation of energy: the heat lost by the metal equals the heat gained by the water. By setting up the equation (mass_metal × c_metal × (100 – 25)) = (mass_water × c_water × (25 – 20)) and using the known value for water’s specific heat capacity, the metal’s specific heat capacity can be calculated.

Example 3: Determining Heat Capacity by the Electrical Method

Question: Explain how you could determine the heat capacity of a liquid using an electrical heater.

Solution:

By supplying a known electrical energy (using the formula Energy = Power × Time) to a known mass of liquid and measuring the temperature change, the heat capacity can be determined using the formula C = Q/ΔT.

Example 4: Application of Newton’s Law of Cooling

Question: Briefly describe how Newton’s Law of Cooling can be used to determine the heat capacity of a substance.

Solution:

Newton’s Law of Cooling relates the rate of temperature change of a body to the difference in temperature between the body and its surroundings. By monitoring the cooling rate and knowing the environmental conditions, the heat capacity can be indirectly determined.

Example 5: Numerical Problem on Heat Capacity

Question: A 100 g sample of water requires 418 J to raise its temperature by 1°C. What is its heat capacity?

Solution:

Heat capacity of the water sample = Q/ΔT = 418 J/1°C = 418 J/°C.

Example 6: Specific Heat Capacity Calculation

Question: If a 200 g sample of a substance requires 840 J of heat to raise its temperature by 2°C, calculate its specific heat capacity.

Solution:

Specific heat capacity, c = Q / (m × ΔT) = 840 J / (0.2 kg × 2°C) = 840 / 0.4 = 2100 J/(kg·°C).

Example 7: Comparing Heat Capacities

Question: Two liquids have the same mass. Liquid A has a higher specific heat capacity than Liquid B. Explain what this means in terms of heat capacity.

Solution:

Since the masses are equal, the liquid with the higher specific heat capacity (Liquid A) will have a greater heat capacity, meaning it requires more heat to raise its temperature by 1°C.

Example 8: Application of the Method of Mixtures

Question: Describe how you would determine the specific heat capacity of an unknown metal using the method of mixtures.

Solution:

Heat the unknown metal to a known temperature, then quickly immerse it in a known mass of water at a lower temperature. Measure the final equilibrium temperature, then apply the energy conservation equation (heat lost by metal = heat gained by water) to solve for the metal’s specific heat capacity.

Example 9: Electrical Method for Determining Heat Capacity

Question: Outline the steps involved in determining the heat capacity of a liquid using the electrical method.

Solution:

Pass a known current through a heater immersed in the liquid for a set time, measure the energy supplied (E = IVt), and record the resulting temperature rise. Then, use the formula C = E/ΔT to calculate the heat capacity.

Example 10: Applying Newton’s Law of Cooling

Question: Explain how Newton’s Law of Cooling can help in determining the specific heat capacity of a substance.

Solution:

By measuring the rate at which a heated substance cools in a controlled environment, and applying Newton’s Law of Cooling, one can determine the time constant and subsequently calculate the specific heat capacity, provided the mass and surface area are known.

30 CBT JAMB Quiz on Quantity of Heat

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