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Assertion Bulk modulus of elasticity of ...

Assertion Bulk modulus of elasticity of gases is pressure dependent.
Reason More the pressure of gas, more is the Bulk modulus of elasticity of gas.

A

If both Assertion and Reason are true and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

C

If Assertion is true but Reason is false.

D

If both Assertion and Reason are false.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding Bulk Modulus of Elasticity**: - The bulk modulus of elasticity (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 expressed as: \[ K = -V \frac{dP}{dV} \] where \( V \) is the volume, \( P \) is the pressure, and \( dV \) is the change in volume. 2. **Assertion Analysis**: - The assertion states that the bulk modulus of elasticity of gases is pressure dependent. This is true because the bulk modulus for gases changes with pressure. 3. **Reason Analysis**: - The reason states that more the pressure of gas, more is the bulk modulus of elasticity of gas. This is also true. In fact, for gases, the bulk modulus can be expressed in terms of pressure: - For an adiabatic process: \[ K = \gamma P \] - For an isothermal process: \[ K = P \] - In both cases, as the pressure (P) increases, the bulk modulus (K) also increases. 4. **Conclusion**: - Since both the assertion and the reason are true, and the reason correctly explains the assertion, we can conclude that the statement is correct. ### Final Answer: Both the assertion and reason are correct, and the reason is a correct explanation of the assertion.

To solve the question, we need to analyze the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding Bulk Modulus of Elasticity**: - The bulk modulus of elasticity (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 expressed as: \[ ...
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