Measurement of Temperature

Thermometers utilize various physical properties that change predictably with temperature. Some common thermometric properties are:

i. Expansion of liquids when heated

One of the most common thermometric properties is the expansion of liquids when heated. Alcohol and mercury are frequently used in thermometers because they expand and contract uniformly with temperature changes.

Example: In a mercury thermometer, mercury expands as the temperature increases, causing it to rise in the tube. The height of the mercury column is used to read the temperature.

The change in the volume of a liquid with temperature can be represented by the following linear expansion formula:

$\Delta V = V_0 \beta \Delta T$

Where:

• $\Delta V$ is the change in volume of the liquid.
• $V_0$ is the initial volume of the liquid.
• $\beta$ is the coefficient of volume expansion of the liquid.
• $\Delta T$ is the change in temperature.

For mercury, the value of $\beta$ is quite large, making it ideal for thermometers.

ii. Expansion of a strip of two metals (bimetallic thermometer)

A bimetallic thermometer uses the principle that two strips of different metals, when heated, expand at different rates. This difference in expansion causes the strip to bend, and this bending is used to measure temperature.

Example: In a bimetallic thermometer, the strip made of two metals (e.g., brass and steel) bends more at higher temperatures due to the differing expansion rates. This bending can be calibrated to provide a temperature reading.

iii. Generation of an electric current when heated (thermoelectric thermometer)

When two different metals are joined together and heated at one of the junctions, they generate an electric current. This is known as the thermoelectric effect, which is used in thermocouples.

The amount of current generated depends on the temperature difference between the two junctions. The relation between the generated voltage (or current) and the temperature difference can be expressed by:

$\Delta V = S \Delta T$

Where:

• $\Delta V$ is the voltage generated by the thermocouple.
• $S$ is the Seebeck coefficient (a constant depending on the metals used).
• $\Delta T$ is the temperature difference between the junctions.

Example: Thermocouples are used in industries to measure high temperatures, such as in furnaces and engines. The voltage generated is directly related to the temperature, and by measuring this voltage, the temperature can be determined.

iv. Change in resistance of a wire (resistor thermometer)

The resistance of certain materials, such as metals, changes with temperature. This property is used in resistance thermometers or RTDs (Resistance Temperature Detectors).

The resistance $R$ of a wire at a temperature $T$ is related to its resistance at a reference temperature $T_0$ by the formula:

$R_T = R_0 (1 + \alpha (T - T_0))$

Where:

• $R_T$ is the resistance at temperature $T$.
• $R_0$ is the resistance at the reference temperature $T_0$.
• $\alpha$ is the temperature coefficient of resistance of the material.
• $T - T_0$ is the temperature difference from the reference temperature.

Example: RTDs are widely used in industrial applications where precise temperature measurements are required, such as in laboratories and manufacturing processes.

Therefore: These measurable physical properties (expansion of liquids, bimetallic strips, thermoelectric effect, and change in resistance) form the foundation for different types of thermometers. Each method utilizes a specific property of matter that changes predictably with temperature to provide an accurate reading.

The fundamental interval of a thermometer is the difference between the upper fixed point and the lower fixed point. These points are essential for calibrating the thermometer to ensure accurate readings.

Lower Fixed Point: The lower fixed point is defined as the temperature of pure melting ice, which occurs at 0°C (273.15 K). It is the temperature at which water transitions from a solid to a liquid state. However, impurities in the ice can cause the melting point of ice to decrease, so the purest form of ice must be used for this reference point.

Upper Fixed Point: The upper fixed point is typically defined as the boiling point of water at standard atmospheric pressure, which occurs at 100°C (373.15 K). This is the temperature at which water transitions from a liquid to a gas.

Therefore: The fundamental interval of a thermometer is the range of temperatures between the melting point of ice (lower fixed point) and the boiling point of water (upper fixed point). This interval is used for calibrating thermometers and for defining temperature scales.

The working principle of a liquid-in-glass thermometer is based on the fact that a liquid expands when heated and contracts when cooled. This property is utilized to measure temperature by observing the rise or fall of a liquid inside a narrow tube as the temperature changes. The liquid used in these thermometers is known as the thermometric liquid.

Examples of Liquid-in-Glass Thermometers:

1. Mercury in Glass Thermometer
2. Alcohol in Glass Thermometer

Both types of thermometers have the following components:

1. Bulb: A small bulb at the base that acts as a reservoir for the liquid.
2. Stem: A fine, narrow tube through which the liquid rises or falls with temperature changes.

Mode of Action: When the temperature increases, the liquid in the bulb expands and rises up the stem, while when the temperature decreases, the liquid contracts and falls back down. The height of the liquid column in the stem corresponds to the temperature and can be calibrated against a known temperature scale, such as Celsius or Fahrenheit.

Comparison between Mercury and Alcohol Thermometers:

Property	Mercury	Alcohol
Conductor of Heat	Good conductor of heat	Fairly good conductor of heat
Expansion	Expands linearly	Expands rapidly
Visibility	Clearly visible	Colorless
Boiling Point	360°C	78°C
Freezing Point	-39°C	-112°C
Glass Wetting	Does not wet glass	Does not wet glass

The liquid-in-glass thermometer works on the principle of thermal expansion and contraction of a liquid. The choice of liquid depends on factors like the temperature range, visibility, and physical properties. Mercury is commonly used for higher temperatures, while alcohol is used for lower temperatures because it freezes at a much lower temperature than mercury.

Water is not commonly used as a thermometric liquid in thermometers, despite being cheap and readily available, for the following reasons:

1. Non-linear Volume Expansion: The volume expansion of water with temperature is not linear, meaning that the change in volume does not correspond proportionally with the change in temperature. For a thermometer to be accurate and reliable, the expansion of the thermometric liquid should be linear with temperature.
2. Water Wets Glass: Water has a tendency to wet the glass of the thermometer, which can cause the liquid to cling to the walls of the capillary tube. This interferes with accurate readings, as the liquid may not rise or fall uniformly within the tube.
3. High Heat Capacity: Water has a high specific heat capacity, meaning it requires a significant amount of heat energy to change its temperature. This makes it less sensitive to small changes in temperature compared to liquids like mercury or alcohol, which respond more quickly to temperature variations.

Therefore: Due to these issues, water is not suitable as a thermometric liquid in most thermometers. Instead, liquids like mercury and alcohol are used because their properties allow for more accurate and reliable temperature measurements.

A clinical thermometer is typically a mercury-in-glass thermometer used to measure human body temperature. As the temperature of the body increases, the mercury expands and rises up the capillary tube of the thermometer. This rise in mercury corresponds to the temperature of the body and is used to read the temperature.

Limitations of Clinical Thermometers:

1. Delicate: Mercury thermometers are delicate and can break easily, especially if dropped. This can pose a safety risk, as mercury is toxic.
2. Infection Spread: Clinical thermometers must be sterilized properly before use to prevent the spread of infections. If not sterilized, they can carry germs from one person to another.
3. Core Body Temperature: Clinical thermometers may not always reflect the core body temperature accurately. For example, they measure the temperature at the mouth, underarm, or rectum, but the core temperature might vary slightly from these readings.

Clinical thermometers are essential for measuring body temperature, but they come with limitations, including fragility, infection risk, and potential inaccuracies in reflecting the true core body temperature.