Exhaustive Notes on Temperature and Heat

Fundamentals of Temperature

The concept of temperature is integrated into daily life, often encountered in weather reports that highlight extremes, such as the lowest temperature reported from Nuwaraeliya and the highest temperature reported from Trincomalee on specific days. Daily observations illustrate the influence of temperature, such as why washed clothes struggle to dry on rainy days compared to warm sunny days. Sensory experiences, like the coolness of eating an ice cream or the warmth of a hot cup of tea, further contextualize this concept.

Temperature is defined as a fundamental property of any material object and is the physical quantity that describes the states of hotness or coldness. For instance, an ice cube possesses a very low temperature, and warm water is characterized by a higher temperature than cold water. Humans can qualitatively assess whether an object's temperature is higher or lower than their own body temperature through the sense of touch. Scientifically, temperature is a measure of the mean kinetic energy possessed by the particles that constitute an object.

Measuring Temperature and Thermometry

While touching objects provides a rough estimation of temperature, it is not a suitable scientific method because it lacks accuracy and cannot provide a standardized numerical value. This led scientists to develop specialized devices for measurement. The thermometer is the device employed for this purpose, with the world's first thermometer being invented by Galileo Galilei around the year $1600\,A.D.$

Modern thermometry often utilizes the glass-mercury thermometer. This device consists of a narrow glass tube connected to a bulb containing mercury. As the temperature rises, the mercury expands and moves up the narrow capillary tube. Because the tube's diameter is very small, even a slight volume expansion results in a clearly visible rise in the column. The temperature is then read from a scale marked on the tube. Mercury is ideal for this purpose because it expands uniformly over a broad range, is a good thermal conductor, and remains liquid from $-39\,^\circ\text{C}$ to $357\,^\circ\text{C}$. However, its use is currently declining due to its inherent toxicity.

Alternative devices include the glass-alcohol thermometer, which is constructed similarly to the mercury version but uses ethyl alcohol (ethanol). Since the melting point of purified ethanol is $-115\,^\circ\text{C}$, it is particularly suited for measuring very low temperatures below $0\,^\circ\text{C}$. Ethanol expands significantly and uniformly with temperature. Because it is naturally colorless, it is dyed with coloring materials to make the liquid column visible. Additionally, digital thermometers are prevalent today. Instead of thermal expansion, these devices use electrical properties, such as resistance that changes with temperature, detected via a sensor called a thermistor to provide a direct digital readout.

Temperature Scales: Celsius, Fahrenheit, and Kelvin

Measurement is standardized through three primary temperature scales: Celsius, Fahrenheit, and Kelvin. The specific temperatures used to establish these scales are known as fixed points. The Celsius scale, introduced by Anders Celsius ($1701$ to $1744$), uses the melting point of pure ice under one atmosphere of pressure as $0\,^\circ\text{C}$ and the vaporization point of water (steam) as $100\,^\circ\text{C}$. These points are highly reliable as they remain fixed values independent of external factors other than pressure variations. This range is divided into $100$ equal divisions.

The Fahrenheit scale, introduced by Gabriel Fahrenheit ($1686$ to $1736$), also uses the melting point of ice and the boiling point of water as its fixed points. In this system, ice melts at $32\,^\circ\text{F}$ and water boils at $212\,^\circ\text{F}$, with the interval between these two points divided into $180$ divisions. Another significant advancement came with Clifford Olbert ($1836$ to $1925$), who constructed the clinical thermometer.

The Kelvin scale is the international unit of measuring temperatures ($\text{K}$) and was introduced by the British scientist Lord Kelvin ($1824$ to $1907$). Kelvin identified that there is a minimum theoretical temperature where the kinetic energy of all particles in an object reaches zero, a state known as absolute zero. This temperature corresponds to $-273.15\,^\circ\text{C}$. The Kelvin scale sets its zero ($0\,\text{K}$) at this absolute zero. On this scale, a temperature difference of $1\,\text{K}$ is equal to a difference of $1\,^\circ\text{C}$. Consequently, the melting point of ice is approximately $273\,\text{K}$ and the boiling point of water is approximately $373\,\text{K}$.

Relationships and Conversions Between Scales

The fundamental difference between the Kelvin and Celsius scales is the chosen zero value. To convert a Celsius value to Kelvin, one must add $273$. To convert Kelvin to Celsius, one must subtract $273$. For example, $50\,^\circ\text{C}$ converts to Kelvin as $50 + 273 = 323\,\text{K}$. Conversely, the boiling point of water at $373\,\text{K}$ converts to Celsius as $373 - 273 = 100\,^\circ\text{C}$. It is important to note that one division on the Celsius scale is exactly equal in magnitude to one division on the Kelvin scale.

Concepts of Heat and Energy Transfer

Heat is described as a form of energy that transfers between objects due to a temperature difference. Benjamin Thompson, also known as Count Rumford ($1753$ to $1814$), was the first to describe heat as a form of energy. In $1798$, he experimentally proved this concept, which was further investigated by James Joule in $1840$. Because heat is energy, its international unit is the Joule ($\text{J}$), though the Calorie is also frequently used.

Heat transfer is demonstrated when a heated block of iron is placed into a vessel of cold water at room temperature. Heat flows from the iron (higher temperature) to the water (lower temperature). The temperature of the water rises as it and the vessel absorb heat, while the iron's temperature decreases. This flow continues until the temperatures equalize, a state known as thermal equilibrium. Once equilibrium is reached, no further net heat transfer occurs between the bodies.

Heat Capacity and its Specific Identification

The amount of heat required to raise the temperature of a substance varies according to its mass and its specific nature. This is illustrated by heating equal volumes of water and coconut oil for the same duration with identical heat sources; despite receiving the same amount of heat, the temperature rises are different. The heat capacity of an object is defined as the amount of heat required to increase its temperature by one unit. The symbol for heat capacity is $C$, and its units are Joules per Kelvin ($\text{JK}^{-1}$) or Joules per degree Celsius ($\text{J}^\circ\text{C}^{-1}$). It depends on both the material of the object and its mass.

Specific heat capacity, denoted by $c$, is a property of the substance itself. It is defined as the amount of heat required to increase the temperature of a unit mass ($1\,\text{kg}$) of a substance by one degree ($1\,\text{K}$ or $1\,^\circ\text{C}$). The relation between heat capacity and specific heat capacity is expressed by the formula: $\text{Heat capacity} = \text{Mass} \times \text{Specific heat capacity}$ or $C = mc$. The units for specific heat capacity are $J\,kg^{-1}\,K^{-1}$ or $J\,kg^{-1}\,^\circ\text{C}^{-1}$. Notable specific heat capacities include water at $4200\,J\,kg^{-1}\,K^{-1}$, ice at $2100\,J\,kg^{-1}\,K^{-1}$, and mercury at $140\,J\,kg^{-1}\,K^{-1}$.

Quantitative Calculation of Heat Flow

To find the quantity of heat ($Q$) absorbed or released by a substance, the following relation is used: $\text{Quantity of heat} (Q) = \text{mass} (m) \times \text{specific heat capacity} (c) \times \text{temperature change} (\theta)$. This is simplified as the equation: $Q = mc\theta$. In this formula, $Q$ is in Joules ($\text{J}$), $m$ is in kilograms ($\text{kg}$), $c$ is the specific heat capacity, and $\theta$ represents the temperature difference in Kelvin or Celsius.

Example calculations illustrate these principles: to raise the temperature of $2\,\text{kg}$ of water by $10\,\text{K}$, the heat required is calculated as $2\,kg \times 4200\,J\,kg^{-1}\,K^{-1} \times 10\,K = 84000\,\text{J}$. For a $500\,\text{g}$ ($0.5\,kg$) block of aluminium heated from $30\,^\circ\text{C}$ to $50\,^\circ\text{C}$ with a specific heat capacity of $900\,J\,kg^{-1}\,^\circ\text{C}^{-1}$, the heat required is $0.5\,kg \times 900\,J\,kg^{-1}\,^\circ\text{C}^{-1} \times (50 - 30)\,^\circ\text{C} = 9000\,\text{J}$. If $20000\,\text{J}$ of heat is transferred to $2\,kg$ of copper ($c = 400\,J\,kg^{-1}\,K^{-1}$) at $30\,^\circ\text{C}$, the temperature change $\theta$ is calculated as $\frac{20000}{2 \times 400} = 25\,^\circ\text{C}$, resulting in a final temperature of $55\,^\circ\text{C}$.

Exercise 9.1 and Discussion

Questions regarding temperature conversion were posed. For Celsius to Kelvin: $10\,^\circ\text{C}$ becomes $283\,\text{K}$, $27\,^\circ\text{C}$ becomes $300\,\text{K}$, $87\,^\circ\text{C}$ becomes $360\,\text{K}$, and $127\,^\circ\text{C}$ becomes $400\,\text{K}$. For Kelvin to Celsius: $0\,\text{K}$ becomes $-273\,^\circ\text{C}$, $100\,\text{K}$ becomes $-173\,^\circ\text{C}$, $273\,\text{K}$ becomes $0\,^\circ\text{C}$, $373\,\text{K}$ becomes $100\,^\circ\text{C}$, and $400\,\text{K}$ becomes $127\,^\circ\text{C}$.

A specific problem was presented involving a copper vessel containing $1\,kg$ of water where the total mass of the vessel and water is $1.6\,kg$. The water is at $25\,^\circ\text{C}$ and needs to be heated until it boils ($100\,^\circ\text{C}$), requiring the use of specific heat capacities for both water ($4200\,J\,kg^{-1}\,K^{-1}$) and copper ($400\,J\,kg^{-1}\,K^{-1}$).