### Problem Explanation: Volume Change in Artificial Diamond Due to Pressure DifferenceArtificial diamonds can be created by using high-pressure, high-temperature presses. Suppose an artificial diamond with a volume of \(1.30 \times 10^{-6} \, \text{m}^3\) is formed under a pressure of \(4.70 \, \text{GPa}\). #### Objective:Find the change in its volume (\( \Delta V \) in \( \text{m}^3 \)) when it is released from the press and brought to atmospheric pressure. #### Given Data:- Initial volume, \( V = 1.30 \times 10^{-6} \, \text{m}^3 \)- Pressure under which it is formed, \( P = 4.70 \, \text{GPa} \)- Bulk modulus of diamond, \( B = 194 \, \text{GPa} \)- Atmospheric pressure is assumed to be negligible compared to the pressure under which the diamond was formed.#### Approach to Solution:1. **Understand Bulk Modulus**: - The bulk modulus \( B \) is a measure of a substance's resistance to uniform compression. - It is given by the formula: \[ B = -\frac{\Delta P}{\frac{\Delta V}{V}} \] Where \( \Delta P \) is the change in pressure and \( \frac{\Delta V}{V} \) is the relative change in volume.2. **Calculate the Change in Volume**: - Rearrange the bulk modulus formula to solve for \( \Delta V \): \[ \frac{\Delta V}{V} = -\frac{\Delta P}{B} \]3. **Substitute Given Values**: - \( \Delta P \approx 4.70 \, \text{GPa} \) (since atmospheric pressure is negligible) - \( B = 194 \, \text{GPa} \) - Calculate \( \frac{\Delta V}{V} \): \[ \frac{\Delta V}{V} = -\frac{4.70}{194} \] \[ \frac{\Delta V}{V} = -0.0242 \] - Thus, \[ \Delta V = V

Given data : pressure under which diamond is kept, P = 4.70 Gpa = 4.7 × 109 Pa Bulk modulus of…

Artificial diamonds can be made using high-pressure, high-temperature presses. Suppose an artificial diamond of volume 1.30 x 10-6 m3 is formed under a pressure of 4.70 GPa. Find the change in its volume (in m³) when it is released from the press and brought to atmospheric pressure. Take the diamond's bulk modulus to be B = 194 GPa. (Assume the system is at sea level.)

Artificial diamonds can be made using high-pressure, high-temperature presses. Suppose an artificial diamond of volume 1.30 x 10-6 m3 is formed under a pressure of 4.70 GPa. Find the change in its volume (in m³) when it is released from the press and brought to atmospheric pressure. Take the diamond's bulk modulus to be B = 194 GPa. (Assume the system is at sea level.)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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