Temperature and its Measurement — NCERT Solutions

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 $= 37.0^\circ\text{C}$

(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: $37.6^\circ\text{C}$

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

(ii) Day and time of highest temperature:

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

(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).