A solid is highly compressible. Is its bulk modulus high?

Answer

To determine whether a solid that is highly compressible has a high bulk modulus, we can analyze the relationship between compressibility and bulk modulus.

### Step-by-Step Solution:

1. **Understanding Compressibility**:
- Compressibility (β) is a measure of how much a material can be compressed under pressure. It is defined as the fractional change in volume per unit increase in pressure.
- Mathematically, it can be expressed as:
\[ \beta = -\frac{1}{V} \frac{dV}{dP} \]
where \( V \) is the volume and \( P \) is the pressure.

2. **Understanding Bulk Modulus**:
- The bulk modulus (K) is a measure of a material's resistance to uniform compression. It is defined as the ratio of the change in pressure to the fractional change in volume.
- Mathematically, it is given by:
\[ K = -V \frac{dP}{dV} \]

3. **Relationship Between Compressibility and Bulk Modulus**:
- There is an inverse relationship between compressibility and bulk modulus:
\[ K = \frac{1}{\beta} \]
This means that if a material has a high compressibility (i.e., it can be compressed easily), its bulk modulus will be low.

4. **Analyzing the Given Statement**:
- The question states that the solid is "highly compressible." This implies that the compressibility (β) is high.
- According to the relationship \( K = \frac{1}{\beta} \), if β is high, then K must be low.

5. **Conclusion**:
- Therefore, if a solid is highly compressible, its bulk modulus cannot be high. The answer to the question is **no**.

### Final Answer:
No, if a solid is highly compressible, its bulk modulus is not high.