# Calculating change in volume (bulk modulus)

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In summary, bulk modulus is a measure of a substance's resistance to compression under pressure. It is important in calculating change in volume because it helps determine how much a substance's volume will change when subjected to external pressure. Bulk modulus is calculated by dividing the change in pressure by the corresponding change in volume and is typically represented by the letter K. It is inversely related to compressibility and cannot be negative. Bulk modulus is used in various real-world applications, including the design of hydraulic systems, determining material elasticity, and studying the properties of rocks and minerals under pressure. It is also essential in industries such as construction, oil and gas, and manufacturing to ensure the stability and strength of materials under different pressures.
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## Homework Statement

a hydraulic system operates at 3000 psi. Compute the percentage change in the volume of the oil in the system as the pressure is increased from zero to 3000 psi if the bulk modulus of the oil is 189000 psi.

E=∆p/(∆V)/V

## The Attempt at a Solution

$189 000 psi = -3000 psi/v$
=-63
which is way off.

ps. by the way is it possible to use the increment symbol (∆) in latex font?

any hints?

## 1. What is bulk modulus and why is it important in calculating change in volume?

Bulk modulus is the measure of a substance's resistance to compression under pressure. It is important in calculating change in volume because it helps determine how much a substance's volume will change when subjected to external pressure.

## 2. How is bulk modulus calculated?

Bulk modulus is calculated by dividing the change in pressure by the corresponding change in volume. It is typically represented by the letter K and has units of pressure, such as pascals (Pa) or pounds per square inch (psi).

## 3. What is the relationship between bulk modulus and compressibility?

Bulk modulus and compressibility are inversely related. This means that substances with higher bulk modulus values are less compressible, while substances with lower bulk modulus values are more compressible.

## 4. Can bulk modulus be negative?

No, bulk modulus cannot be negative. It is a measure of a substance's resistance to compression, so a negative value would indicate that the substance is expanding under pressure.

## 5. How is bulk modulus used in real-world applications?

Bulk modulus is used in a variety of real-world applications, such as in the design of hydraulic systems, determining the elasticity of materials, and in geology to study the properties of rocks and minerals under pressure. It is also used in industries such as construction, oil and gas, and manufacturing to ensure the stability and strength of materials under different pressures.

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