Choose the correct statements from the following:

Options

A. (a)A temperature change which increases the length of a steel rod by `0.1%` will increase its volume by nearly `0.3%`
B. (b)The specific heat of a solid is different when the solid is heated at (i) constant pressure and (ii) the constant volume
C. (c)the thermal conductivity of air being less than that for wool, we prefer wool to air for thermal insulation
D. (d)When the distance between two fixed points is measured with a steel tape, the observed reding will be less on a hot day than on a cold day

Explanation

To solve the problem of choosing the correct statements from the given options A, B, C, and D, we will analyze each statement one by one.

### Step 1: Analyze Statement A
**Statement A:** "Temperature changes with increase the length of a steel rod by 0.1 percent will increase its volume nearly 0.3 percent."

- The coefficient of volume expansion is approximately three times the coefficient of linear expansion.
- If the length of the rod increases by 0.1%, the volume increase can be calculated as:
\[ \text{Volume change} \approx 3 \times \text{Length change} = 3 \times 0.1\% = 0.3\% \]
- Thus, Statement A is **correct**.

### Step 2: Analyze Statement B
**Statement B:** "The specific heat of a solid is different when the solid is heated at constant pressure and at constant volume."

- When a solid is heated at constant pressure, it does expand slightly, and some heat is used for doing mechanical work.
- The difference between specific heat at constant pressure (Cp) and constant volume (Cv) is generally negligible for solids and liquids, but significant for gases.
- Therefore, Statement B is **correct**.

### Step 3: Analyze Statement C
**Statement C:** "The thermal conductivity of air being less than that of wool, we prefer wool to air for thermal insulation."

- Although the thermal conductivity of air is indeed less than that of wool, wool is preferred for insulation because it traps air pockets.
- These air pockets reduce heat transfer by conduction and convection, making wool a better insulator than air alone.
- Therefore, Statement C is **incorrect**.

### Step 4: Analyze Statement D
**Statement D:** "When the distance between two fixed points is measured with a steel tape, the observer's reading will be less on a hot day than on a cold day."

- On a hot day, the steel tape expands due to the increase in temperature, causing the distance between the fixed points to appear longer.
- Consequently, the reading will be less on a hot day than on a cold day because the tape expands and the markings are further apart.
- Therefore, Statement D is **correct**.

### Conclusion
The correct statements are:
- A: Correct
- B: Correct
- C: Incorrect
- D: Correct

Thus, the final answer is that statements A, B, and D are correct.

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