Temperature and its Measurement

Correct option: (ii) 37.0 °C

The normal body temperature of a healthy human adult is taken to be 37.0 °C (which is equal to 98.6 °F on the Fahrenheit scale). 98.6 °C would be dangerously high, and 32.0 °C or 27.0 °C are far below normal body temperature.

Correct option: (iv) 98.6 °F

Given: Temperature $= 37^\circ\text{C}$

Formula used:
$$^\circ\text{F} = \frac{9}{5} \times {^\circ\text{C}} + 32$$

Calculation:
$$^\circ\text{F} = \frac{9}{5} \times 37 + 32 = \frac{333}{5} + 32 = 66.6 + 32 = 98.6^\circ\text{F}$$

Answer: $37^\circ\text{C} = 98.6^\circ\text{F}$

(i) The hotness or coldness of a system is determined by its temperature.

*Explanation:* Temperature is the physical quantity that tells us how hot or cold a body or system is.

(ii) The temperature of ice-cold water cannot be measured by a clinical thermometer.

*Explanation:* A clinical thermometer has a limited range (typically $35^\circ\text{C}$ to $42^\circ\text{C}$), which is designed only for measuring human body temperature. Ice-cold water is around $0^\circ\text{C}$, which is far below this range.

(iii) The unit of temperature is degree Celsius (or degree Fahrenheit / kelvin, depending on the scale used).

*Explanation:* The most commonly used unit in everyday life is degree Celsius ($^\circ\text{C}$). The SI unit of temperature is kelvin (K).

Correct option: (ii) $-10^\circ\text{C}$ to $110^\circ\text{C}$

A laboratory thermometer is designed to measure a wide range of temperatures in experiments. Its typical range is from $-10^\circ\text{C}$ to $110^\circ\text{C}$. The range $35^\circ\text{C}$–$42^\circ\text{C}$ belongs to a clinical thermometer, while $32^\circ\text{C}$–$45^\circ\text{C}$ is too narrow for laboratory use.

Correct option: (ii) Student 2

Reasoning: The correct way to measure temperature using a laboratory thermometer requires:
1. The thermometer must be held vertically (not tilted).
2. The bulb must be immersed in the liquid but must not touch the bottom or sides of the beaker.
3. The temperature must be read while the thermometer is still immersed in the liquid.
4. The eye must be directly in line (horizontal) with the level of the liquid column.

Student 2 follows all these precautions correctly. The other students either tilt the thermometer, remove it from water before reading, or read it at an incorrect angle.

Note: This is a drawing/colouring activity. Since the specific temperature values written below Fig. 7.7 are not fully visible in the OCR text, the general method is described below.

Method to shade the thermometer column:
1. Identify the temperature value given (e.g., $37^\circ\text{C}$, $0^\circ\text{C}$, $100^\circ\text{C}$, etc.).
2. Locate that value on the Celsius scale marked on the thermometer drawing.
3. Colour (shade in red) the column from the bottom of the bulb up to the mark corresponding to the given temperature.

Example: If the temperature is $37^\circ\text{C}$, shade the column from the bulb up to the $37^\circ\text{C}$ mark on the scale.

*(Note: The figure shows a clinical thermometer based on the scale markings visible in the OCR context — range approximately 35 °C to 42 °C.)*

(i) Type of thermometer:
It is a clinical thermometer.

*Reason:* The scale range (approximately $35^\circ\text{C}$ to $42^\circ\text{C}$) is characteristic of a clinical thermometer used to measure human body temperature.

(ii) Reading of the thermometer:
Based on the figure, the reading is approximately $37.0^\circ\text{C}$ (the exact value depends on where the liquid column ends in Fig. 7.8; students should read the value where the top of the liquid column aligns with the scale).

(iii) Smallest value this thermometer can measure:

Given: The two bigger marks are $1^\circ\text{C}$ apart, and there are typically 10 small divisions between them.

$$\text{Smallest division} = \frac{1^\circ\text{C}}{10} = 0.1^\circ\text{C}$$

The smallest value that this thermometer can measure is $\mathbf{0.1^\circ\text{C}}$.

Answer:

A laboratory thermometer is not suitable for measuring body temperature for the following reasons:

1. Range mismatch: A laboratory thermometer has a range of $-10^\circ\text{C}$ to $110^\circ\text{C}$. Human body temperature lies between $35^\circ\text{C}$ and $42^\circ\text{C}$. Although this range falls within the laboratory thermometer's scale, the divisions are too large (smallest division = $1^\circ\text{C}$) to give an accurate reading of body temperature.

2. Lack of kink: A clinical thermometer has a kink (constriction) near the bulb that prevents the mercury/liquid from falling back when the thermometer is taken out of the mouth. A laboratory thermometer does not have this kink, so the liquid column falls back immediately upon removal, making it impossible to read the temperature outside the body.

3. Safety concern: A laboratory thermometer is not designed to be placed in the mouth; it is fragile and not hygienic for clinical use.

Conclusion: Due to the absence of a kink and its larger least count, a laboratory thermometer cannot give an accurate and stable reading of body temperature.

Given data: Body temperature of Vaishnavi over three days at different times.

Normal body temperature $= 37.0^\circ\text{C}$

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(i) Highest recorded temperature:

Looking at all the values in the table:
- Day One maximum: $40.0^\circ\text{C}$ (at 7 pm)
- Day Two maximum: $39.0^\circ\text{C}$
- Day Three maximum: $37.6^\circ\text{C}$

$$\text{Highest recorded temperature} = \mathbf{40.0^\circ\text{C}}$$

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(ii) Day and time of highest temperature:

The temperature $40.0^\circ\text{C}$ was recorded on Day One at 7 pm.

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(iii) Day on which temperature returned to normal:

Normal body temperature $= 37.0^\circ\text{C}$.

On Day Three, at 4 pm, the temperature reads exactly $37.0^\circ\text{C}$, and it continues to fall below $37.0^\circ\text{C}$ after that.

Therefore, Vaishnavi's temperature returned to normal on Day Three (at 4 pm).

Given: Temperature to be measured $= 22.5^\circ\text{C}$

*(Note: Fig. 7.9 shows three thermometers with different least counts. Based on standard NCERT content, the three thermometers typically have least counts of $1^\circ\text{C}$, $0.5^\circ\text{C}$, and $0.1^\circ\text{C}$ respectively.)*

Analysis:

- A thermometer with least count $1^\circ\text{C}$ can only read whole numbers like $22^\circ\text{C}$ or $23^\circ\text{C}$. It cannot read $22.5^\circ\text{C}$.
- A thermometer with least count $\mathbf{0.5^\circ\text{C}}$ can read values like $22.0^\circ\text{C}$, $22.5^\circ\text{C}$, $23.0^\circ\text{C}$, etc. It can read $22.5^\circ\text{C}$.
- A thermometer with least count $0.1^\circ\text{C}$ can also read $22.5^\circ\text{C}$, but it is more precise than needed.

Conclusion: The thermometer with a least count of $0.5^\circ\text{C}$ should be used to measure $22.5^\circ\text{C}$, as it is the most appropriate choice — it can measure this value accurately without being unnecessarily precise.

Correct option: (ii) $27.5^\circ\text{C}$

Reasoning:
In Fig. 7.10, the liquid column ends between the $27^\circ\text{C}$ and $28^\circ\text{C}$ marks. If the thermometer has a least count of $0.5^\circ\text{C}$ (i.e., 2 divisions per degree), the column ending at the midpoint between $27^\circ\text{C}$ and $28^\circ\text{C}$ gives a reading of:
$$\text{Temperature} = 27^\circ\text{C} + 0.5^\circ\text{C} = \mathbf{27.5^\circ\text{C}}$$

Given:
- Number of divisions between $0^\circ\text{C}$ and $100^\circ\text{C}$ $= 50$
- Temperature difference $= 100^\circ\text{C} - 0^\circ\text{C} = 100^\circ\text{C}$

Formula:
$$\text{Value of each division} = \frac{\text{Total temperature difference}}{\text{Number of divisions}}$$

Calculation:
$$\text{Value of each division} = \frac{100^\circ\text{C}}{50} = 2^\circ\text{C}$$

Answer: Each division of this thermometer measures $\mathbf{2^\circ\text{C}}$.

Given: Smallest division $= 0.5^\circ\text{C}$; Draw scale from $10^\circ\text{C}$ to $20^\circ\text{C}$.

Working:

Since the smallest division $= 0.5^\circ\text{C}$, between any two consecutive degree marks (e.g., $10^\circ\text{C}$ and $11^\circ\text{C}$), there will be:
$$\text{Number of divisions} = \frac{1^\circ\text{C}}{0.5^\circ\text{C}} = 2 \text{ divisions}$$

So between $10^\circ\text{C}$ and $20^\circ\text{C}$, there will be:
$$\text{Total divisions} = \frac{10^\circ\text{C}}{0.5^\circ\text{C}} = 20 \text{ divisions}$$

Description of the scale to draw:

```
|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|
10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20
```

- Draw a vertical line (the thermometer tube).
- Mark longer lines at every whole degree: $10, 11, 12, \ldots, 20$.
- Mark shorter lines at every $0.5^\circ\text{C}$ interval: $10.5, 11.5, 12.5, \ldots, 19.5$.
- Label the longer marks with the degree values.

This gives a scale where the smallest readable division is $0.5^\circ\text{C}$.

Answer: Komal means 101 degrees on the Fahrenheit scale ($101^\circ\text{F}$).

Reasoning:

- Normal body temperature $= 37^\circ\text{C} = 98.6^\circ\text{F}$
- A fever of $101^\circ\text{C}$ is impossible for a living human being — water boils at $100^\circ\text{C}$, so a body temperature of $101^\circ\text{C}$ would be fatal and physically impossible.
- However, $101^\circ\text{F}$ is a mild fever, which is slightly above the normal body temperature of $98.6^\circ\text{F}$. This is a common and realistic fever temperature.

Verification:
$$101^\circ\text{F} \rightarrow ^\circ\text{C} = \frac{5}{9} \times (101 - 32) = \frac{5}{9} \times 69 = 38.3^\circ\text{C}$$

$38.3^\circ\text{C}$ is indeed a mild fever, which is medically reasonable.

Conclusion: Komal means $101^\circ\text{F}$ (Fahrenheit scale).