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Chapter 7: Temperature And Its Measurement
1. Understanding Hot and Cold
In our daily lives, we often compare the hotness or coldness of objects. For instance, water in an earthen matka is cooler than tap water during an Indian summer. However, science teaches us that our sense of touch is not a reliable tool for measurement.
Why Sense of Touch Fails
As explored in Activity 7.1, the sensation of heat is relative to our previous experience. This is demonstrated using three containers:
- Container A: Warm water.
- Container B: Tap water.
- Container C: Ice-cold water.
When you move your hands from containers A and C into B simultaneously:
- The hand from warm water feels the tap water is cold.
- The hand from cold water feels the same tap water is warm.
Conclusion: To find out exactly how hot or cold a body is, we need a standard measure called Temperature.
Types of Thermometers
A Thermometer is the device used to measure temperature. There are several varieties used in the Indian context:
- Digital Clinical Thermometer: Used for measuring human body temperature; safe and easy to read.
- Laboratory Thermometer: Used for scientific experiments (Range: $-10 \ ^{\circ}\text{C}$ to $110 \ ^{\circ}\text{C}$).
- Infrared Thermometer: A non-contact device that uses sensors to measure temperature from a distance, frequently used during the COVID-19 pandemic.
2. Clinical Thermometers and Body Temperature
A Clinical Thermometer is specifically designed to measure the temperature of the human body. In India, most households have now shifted from mercury thermometers to digital thermometers.
The Shift to Digital Thermometers
- Safety First: Mercury is highly toxic and extremely difficult to dispose of if the glass breaks.
- Easy Reading: Digital displays show the temperature in numbers, removing the need to look for a thin mercury thread.
- Sensors: Digital versions use heat sensors to provide an accurate reading.
What is "Normal" Temperature?
The standard normal temperature of a healthy human body is taken as $37.0 \ ^{\circ}\text{C}$. However, it is important to remember:
- It is an average body temperature of a large number of healthy people.
- Individual temperatures may be slightly higher or lower than $37.0 \ ^{\circ}\text{C}$.
- Influencing Factors: Temperature varies based on age, time of the day, and physical activity level.
- Range: A human's body temperature rarely falls below $35 \ ^{\circ}\text{C}$ or rises above $42 \ ^{\circ}\text{C}$.
Steps to Measure Body Temperature
- Wash the tip of the thermometer with soap and water (avoiding the display area).
- Press the reset button.
- Place it under the tongue (for adults) or in the armpit (for children/elderly).
- Wait for the beeping sound.
- Read the display and record the value with the unit ($^{\circ}\text{C}$).
Example 1. A student buys a digital thermometer for $\text{₹} \ 250$ to check his sister's fever. The display shows $39.5 \ ^{\circ}\text{C}$. If the normal body temperature is $37.0 \ ^{\circ}\text{C}$, by how many degrees is her temperature higher?
Answer:
To find the difference in temperature, we subtract the normal temperature from the observed reading:
$\text{Difference} = 39.5 \ ^{\circ}\text{C} - 37.0 \ ^{\circ}\text{C}$
$\text{Difference} = 2.5 \ ^{\circ}\text{C}$
The temperature is $2.5 \ ^{\circ}\text{C}$ higher than normal, indicating a significant fever.
3. Scales of Temperature
Temperature can be measured on different scales, much like length can be measured in metres or inches. The three major scales are named after the scientists who developed them.
Comparison of Temperature Scales
- Celsius Scale ($^{\circ}\text{C}$): The most widely used scale in India for daily and weather reports. Freezing point of water is $0 \ ^{\circ}\text{C}$ and Boiling point is $100 \ ^{\circ}\text{C}$.
- Fahrenheit Scale ($^{\circ}\text{F}$): Historically used for clinical purposes. The normal body temperature of $37.0 \ ^{\circ}\text{C}$ is equivalent to $98.6 \ ^{\circ}\text{F}$.
- Kelvin Scale ($\text{K}$): The SI unit of temperature used in scientific work. It does not use the degree ($^{\circ}$) symbol.
Writing and Conversion Rules
- Conversion: To convert Celsius to Kelvin, use the formula:
$\text{Temperature in K} = \text{Temperature in } ^{\circ}\text{C} + 273.15$
- Capitalization: Scale names (Celsius, Kelvin) start with a capital letter, but the unit (kelvin) starts with a lower-case letter.
- Spacing: Always leave a space between the number and the unit (e.g., $310 \ \text{K}$).
Temperature Reference Table
The following table compares the normal human body temperature across the three scales:
| Scale Name | Value | Symbol |
|---|---|---|
| Celsius | $37.0$ | $^{\circ}\text{C}$ |
| Fahrenheit | $98.6$ | $^{\circ}\text{F}$ |
| Kelvin (SI Unit) | $310.15$ | $\text{K}$ |
4. The Laboratory Thermometer
While clinical thermometers are designed for the human body, scientific experiments require a much larger range. For this, we use the Laboratory Thermometer. It is commonly used in schools and research facilities across India to measure the temperature of various substances.
Construction and Working
- It consists of a long, narrow, and uniform glass tube that is vacuum-sealed.
- At the bottom end, there is a bulb containing a liquid, usually mercury or red-colored alcohol.
- The liquid column expands and rises up the capillary tube when it comes in contact with a hot object and contracts when cooled.
- The Range of a standard laboratory thermometer is typically from $-10 \ ^{\circ}\text{C}$ to $110 \ ^{\circ}\text{C}$.
Derivation of Least Count
The Least Count is the smallest value of temperature that can be accurately measured by the thermometer. To calculate it, we follow these steps:
- Step 1: Identify the temperature difference between two consecutive big marks. Let this be $D$. For most lab thermometers, $D = 10 \ ^{\circ}\text{C}$.
- Step 2: Count the number of small divisions ($n$) between these two big marks. Usually, $n = 10$.
- Step 3: Apply the formula:
$\text{Smallest value (Least Count)} = \frac{\text{Difference between big marks}}{\text{Number of small divisions}}$
- Step 4: Calculation:
$\text{Least Count} = \frac{10 \ ^{\circ}\text{C}}{10} = 1 \ ^{\circ}\text{C}$
Precautions for Accurate Measurement
To ensure that the measurements are correct and the glass does not break, follow these guidelines:
- Vertical Alignment: Always hold the thermometer vertically. Do not tilt it.
- Bulb Position: The bulb must be fully immersed in the substance being measured.
- No Contact: The bulb should not touch the bottom or the sides of the beaker or container.
- Read while Immersed: Unlike a clinical thermometer, the reading must be taken while the bulb is still inside the liquid. The level falls as soon as it is removed.
- Eye Level: Keep your eye directly in line with the top of the liquid column to avoid parallax error.
5. Temperatures of Boiling Water and Ice
A fascinating scientific fact is that the temperature of water remains constant during its phase change (boiling or melting), even if heat is continuously provided.
Phase Change Constants
Under standard atmospheric pressure at sea level, the fixed points for pure water are:
- Melting Point of Ice: $0 \ ^{\circ}\text{C}$
- Boiling Point of Water: $100 \ ^{\circ}\text{C}$
Regional Variation: The Shillong Experiment
The boiling point of water decreases as we go higher above sea level. Students in Shillong (Meghalaya) conducted an experiment to find the boiling point of water. Their results are summarized below:
| Student Name | Phiban | Shemphang | Onestar | Kloi | Bandarisha |
| Boiling Point ($^{\circ}\text{C}$) | $97.8$ | $98.0$ | $97.9$ | $98.0$ | $98.1$ |
The average boiling point in this high-altitude region is approximately $98 \ ^{\circ}\text{C}$, which is lower than the $100 \ ^{\circ}\text{C}$ observed in coastal areas like Mumbai or Chennai.
6. Air Temperature and Weather Monitoring
Air temperature is a critical parameter that affects agriculture, health, and disaster management in India. Weather reports usually mention the Maximum and Minimum temperatures recorded over $24$ hours.
Indian Scientist: Anna Mani
Anna Mani ($1918–2001$), known as the 'Weather Woman of India', was a pioneer in meteorology. Her contributions include:
- Building a large number of indigenous weather-measuring instruments, making India self-reliant.
- Researching solar and wind energy, which paved the way for India's leadership in renewable resources.
- Establishing systems to monitor air temperature and ozone levels across the Indian subcontinent.
Tracking Daily Temperature
Air temperature varies throughout the day. Below is a sample record of daily air temperatures for a city like Nagpur during early summer:
| Day | Max Temperature ($^{\circ}\text{C}$) | Min Temperature ($^{\circ}\text{C}$) |
|---|---|---|
| Day 1 | $40$ | $26$ |
| Day 2 | $41$ | $27$ |
| Day 3 | $42$ | $28$ |
| Day 4 | $43$ | $29$ |
| Day 5 | $42$ | $28$ |
| Average | $41.6 \ ^{\circ}\text{C}$ | $27.6 \ ^{\circ}\text{C}$ |
Example 2. A weather report for New Delhi recorded a maximum temperature of $42 \ ^{\circ}\text{C}$ and a minimum of $28 \ ^{\circ}\text{C}$. Convert the maximum temperature into the Kelvin scale using the appropriate scientific formula.
Answer:
To convert temperature from the Celsius scale ($^{\circ}\text{C}$) to the Kelvin scale ($\text{K}$), we use the following relation:
$\text{Temperature in Kelvin (K)} = \text{Temperature in Celsius (}^{\circ}\text{C}) + 273.15$
Given:
$\text{Max Temperature } (t) = 42 \ ^{\circ}\text{C}$
Calculation:
$T (\text{K}) = 42 + 273.15$
$T (\text{K}) = 315.15 \ \text{K}$
The maximum temperature in New Delhi on the Kelvin scale is $315.15 \ \text{K}$.
Let us enhance our learning
Question 1. The normal temperature of a healthy human being is close to ________.
(i) $98.6 \text{ °C}$
(ii) $37.0 \text{ °C}$
(iii) $32.0 \text{ °C}$
(iv) $27.0 \text{ °C}$
Answer:
Question 2. $37 \text{ °C}$ is the same temperature as ________.
(i) $97.4 \text{ °F}$
(ii) $97.6 \text{ °F}$
(iii) $98.4 \text{ °F}$
(iv) $98.6 \text{ °F}$
Answer:
Question 3. Fill in the blanks:
(i) The hotness or coldness of a system is determined by its _________.
(ii) The temperature of ice-cold water cannot be measured by a _________ thermometer.
(iii) The unit of temperature is degree _________.
Answer:
Question 4. The range of a laboratory thermometer is usually .
(i) $10 \text{ °C}$ to $100 \text{ °C}$
(ii) $-10 \text{ °C}$ to $110 \text{ °C}$
(iii) $32 \text{ °C}$ to $45 \text{ °C}$
(iv) $35 \text{ °C}$ to $42 \text{ °C}$
Answer:
Question 5. Four students used a laboratory thermometer to measure the temperature of water as shown in Fig. 7.6:
Who do you think followed the correct way for measuring temperature?
(i) Student 1
(ii) Student 2
(iii) Student 3
(iv) Student 4
Answer:
Question 6. Colour to show the red column on the drawings of thermometers (Fig. 7.7) as per the temperatures written below:
Answer:
Question 7. Observe the part of thermometer shown in Fig. 7.8 and answer the following questions:
(i) What type of thermometer is it?
(ii) What is the reading of the thermometer?
(iii) What is the smallest value that this thermometer can measure?
Answer:
Question 8. A laboratory thermometer is not used to measure our body temperature. Give a reason.
Answer:
Question 9. Vaishnavi has not gone to school as she is ill. Her mother has kept a record of her body temperature for three days as shown in Table 7.4.
| DAY | 7am | 10am | 1pm | 4pm | 7pm | 10pm |
|---|---|---|---|---|---|---|
| One | $38.0 \text{ °C}$ | $37.8 \text{ °C}$ | $38.0 \text{ °C}$ | $38.0 \text{ °C}$ | $40.0 \text{ °C}$ | $39.0 \text{ °C}$ |
| Two | $38.6 \text{ °C}$ | $38.8 \text{ °C}$ | $39.0 \text{ °C}$ | $39.0 \text{ °C}$ | $39.0 \text{ °C}$ | $38.0 \text{ °C}$ |
| Three | $37.6 \text{ °C}$ | $37.4 \text{ °C}$ | $37.2 \text{ °C}$ | $37.0 \text{ °C}$ | $36.8 \text{ °C}$ | $36.6 \text{ °C}$ |
(i) What was Vaishnavi’s highest recorded temperature?
(ii) On which day and at what time was Vaishnavi’s highest temperature recorded?
(iii) On which day did Vaishnavi’s temperature return to normal?
Answer:
Question 10. If you have to measure the temperature $22.5 \text{ °C}$, which of the following three thermometers will you use (Fig. 7.9)? Explain.
Answer:
Question 11. The temperature shown by the thermometer in Fig. 7.10 is
(i) $28.0 \text{ °C}$
(ii) $27.5 \text{ °C}$
(iii) $26.5 \text{ °C}$
(iv) $25.3 \text{ °C}$
Answer:
Question 12. A laboratory thermometer has 50 divisions between $0 \text{ °C}$ and $100 \text{ °C}$. What does each division of this thermometer measure?
Answer:
Question 13. Draw the scale of a thermometer in which the smallest division reads $0.5 \text{ °C}$. You may draw only the portion between $10 \text{ °C}$ and $20 \text{ °C}$.
Answer:
Question 14. Someone tells you that she has a fever of 101 degrees. Does she mean it on the Celsius scale or Fahrenheit scale?
Answer: