Temperature, Quantity of Heat, and Heat Capacity Revision Notes for HSC SSCE Chemistry

Temperature, Quantity of Heat, and Heat Capacity

Introduction

When conducting experiments involving chemical reactions, we often measure temperature changes. However, what chemists really need to know is the quantity of heat or energy involved. Temperature and quantity of heat are related but distinct concepts that are essential to understand in thermochemistry.

Understanding temperature

We naturally sense whether something feels hot or cold through our physiological sensations. Temperature is the scientific measurement we use to quantify how hot or cold an object or substance is. The hotter an object, the higher its temperature reading.

When two objects at different temperatures come into contact, heat flows from the hotter object to the colder one. This heat transfer continues until both objects reach the same temperature—a state called thermal equilibrium.

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Temperature is measured on scales such as Celsius (°C) or Kelvin (K). For temperature changes, a change of 1°C equals a change of 1 K.

Quantity of heat vs temperature

While temperature tells us how hot something is, the quantity of heat (or amount of heat) tells us how much thermal energy an object contains. This is a crucial distinction: two objects can be at exactly the same temperature yet contain very different amounts of heat energy.

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Classic Example: The Red-Hot Pin and Horseshoe

Consider a red-hot pin and a red-hot horseshoe. Both glow red, indicating they're at the same high temperature. However, the horseshoe contains far more heat energy than the tiny pin because of its much greater mass.

Experimental demonstration

A simple experiment illustrates how quantity of heat depends on both mass and the nature of the substance:

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Experimental Demonstration: Heat Capacity and Mass

Setup: Three well-insulated beakers each contain 100 g of water at 25.0°C.

Beaker A: Add 10 g of water at 100°C → Final temperature: 32.0°C
Beaker B: Add 20 g of water at 100°C → Final temperature: 37.5°C
Beaker C: Add 20 g of copper at 100°C → Final temperature: 26.5°C

Observations and Conclusions:

Comparing beakers A and B: The final temperature in beaker B (37.5°C) is higher than in beaker A (32.0°C). Since both started with the same amount of water at 25.0°C, the 20 g of hot water must have contained more heat than the 10 g of hot water.

First principle: The amount of heat energy is proportional to the mass of the substance.

Comparing beakers B and C: Both had 20 g of material at 100°C added, but beaker B (with water) reached a much higher final temperature (37.5°C) than beaker C (with copper) at 26.5°C. This shows that 20 g of water at 100°C contains more heat than 20 g of copper at 100°C.

Second principle: The amount of heat energy in equal masses of different substances depends on the nature of the substances involved.

Specific heat capacity

To quantify how different substances store and transfer heat, we use a property called specific heat capacity.

Definition: The specific heat capacity ( $c$ ) of a substance is the amount of heat required to increase the temperature of one unit of mass of that substance by exactly 1°C (or 1 K).

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Units of Specific Heat Capacity

Specific heat capacity is measured in:

Joules per kelvin per gram: $\text{J K}^{-1} \text{g}^{-1}$
Joules per kelvin per kilogram: $\text{J K}^{-1} \text{kg}^{-1}$

In HSC Chemistry, you'll typically use $\text{J K}^{-1} \text{kg}^{-1}$ , but be aware that data tables may use $\text{J K}^{-1} \text{g}^{-1}$ .

Specific heat capacities of common substances

Different substances have different specific heat capacities, which explains why they heat up and cool down at different rates.

Substance	Specific Heat Capacity ( $\text{J K}^{-1} \text{g}^{-1}$ )	Substance	Specific Heat Capacity ( $\text{J K}^{-1} \text{g}^{-1}$ )
Water (l)	4.18	Calcium carbonate (s)	0.82
Aluminium (s)	0.90	Potassium hydroxide (s)	1.18
Carbon (s)	0.72	Hydrogen peroxide (l)	2.62
Copper (s)	0.39	Ethanol (l)	2.44
Iron (s)	0.45	Ethylene glycol (l)	2.39
Mercury (l)	0.14	Octane (in petrol) (l)	2.22
Sulphur (s)	0.70	Acetone (l)	2.17
Sodium chloride (s)	0.85	Acetic acid (l)	2.03

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Notable Observations from the Table:

Water has the highest specific heat capacity (4.18 $\text{J K}^{-1} \text{g}^{-1}$ ) of all common substances. This is why water is excellent for cooling systems and why coastal areas have moderated climates.
Metals generally have low specific heat capacities (copper is only 0.39). This is why metal objects heat up and cool down quickly.
Organic liquids have intermediate values, typically between 2.0 and 2.6.

The measurement and calculation of heat changes using specific heat capacity is called calorimetry.

Calculating quantities of heat

The heat equation

When a substance undergoes a temperature change, we can calculate the quantity of heat involved using:

$q = mc\Delta T \quad \text{...(14.1)}$

Where:

$q$ = quantity of heat (measured in joules, J)
$m$ = mass of the substance (in grams or kilograms)
$c$ = specific heat capacity of the substance ( $\text{J K}^{-1} \text{g}^{-1}$ or $\text{J K}^{-1} \text{kg}^{-1}$ )
$\Delta T$ = change in temperature (in °C or K)

Understanding temperature change

The change in temperature is calculated as:

$\Delta T = T_{\text{final}} - T_{\text{initial}}$

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Sign Conventions (Very Important for Exams):

If temperature increases: $\Delta T$ is positive, therefore $q$ is positive
→ This means the object has gained heat (endothermic process)
If temperature decreases: $\Delta T$ is negative, therefore $q$ is negative
→ This means the object has lost heat (exothermic process)

Worked example: heating water

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Worked Example: Calculating Heat Required to Warm Water

Question: Calculate the quantity of heat needed to increase the temperature of 155 g of water from 17.0°C to 35.5°C.

Solution:

Given information:

Mass of water: $m = 155 \text{ g}$
Specific heat capacity of water: $c = 4.18 \text{ J K}^{-1} \text{g}^{-1}$
Initial temperature: $T_i = 17.0°\text{C}$
Final temperature: $T_f = 35.5°\text{C}$

Step 1: Calculate the temperature change

$\Delta T = T_f - T_i = 35.5 - 17.0 = 18.5 \text{ K (or 18.5°C)}$

Step 2: Apply the heat equation

$q = mc\Delta T$

$q = 155 \times 4.18 \times 18.5 \text{ g} \cdot \text{J K}^{-1} \text{g}^{-1} \cdot \text{K}$

$q = 1.20 \times 10^4 \text{ J} = 12.0 \text{ kJ}$

Answer: 1.20 × 10⁴ J (or 12.0 kJ) of heat is required.

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Exam Tips:

Always include units with your quantities to ensure they combine correctly
Remember that for temperature changes, 1°C = 1 K
Watch the units for specific heat capacity—be ready to convert between $\text{J K}^{-1} \text{kg}^{-1}$ and $\text{J K}^{-1} \text{g}^{-1}$ as needed
Show your working clearly, including the substitution of values into the equation

Practice problem

Calculate the quantity of heat needed to increase the temperature of 25.3 g of mercury from 18°C to 55°C. (The specific heat capacity of mercury is 0.14 $\text{J K}^{-1} \text{g}^{-1}$ )

Hint: Use the same method as the worked example above. Calculate $\Delta T$ first, then substitute all values into $q = mc\Delta T$ .

Remember!

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Key Points to Remember:

Temperature measures how hot or cold something is, while quantity of heat measures the total thermal energy content.
Two objects at the same temperature can contain very different amounts of heat energy.
The amount of heat in an object depends on both its mass and the nature of the substance (its specific heat capacity).
Specific heat capacity ( $c$ ) is the heat required to raise the temperature of unit mass by 1°C or 1 K. Water has the highest value at 4.18 $\text{J K}^{-1} \text{g}^{-1}$ .
Use the equation $q = mc\Delta T$ to calculate heat quantities, where $\Delta T = T_{\text{final}} - T_{\text{initial}}$ .
Positive $q$ means heat gained (temperature increased); negative $q$ means heat lost (temperature decreased).

Temperature, Quantity of Heat, and Heat Capacity (HSC SSCE Chemistry): Revision Notes