   Chapter 9, Problem 68P

Chapter
Section
Textbook Problem

Artificial diamonds can be made using high-pressure, high-temperature presses. Suppose an artificial diamond of volume 1.00 × 10−6 m3 is formed under a pressure of 5.00 GPa. Find the change in its volume when it is released from the press and brought to atmospheric pressure. Take the diamond’s bulk modulus to be B = 194 GPa.

To determine
The change in volume of the artificial diamonds when it released from the press.

Explanation
The bulk modulus is defined as ΔP=B(ΔV/V) and now the change in volume is ΔV=[V(ΔP)/B] .

Given info: The artificial diamond volume is 1.00×108m3 , the pressure due to press is 5.00GPa , atmospheric pressure is 1.01×105Pa , and the bulk modulus of the diamond is 194GPa .

The formula for the change in volume of the artificial diamond is,

ΔV=V(PfPi)B

• V is volume of the artificial diamond.
• Pi and Pf are initial and final pressures on the diamond.
• B is bulk modulus of the diamond.

Substitute 1.00×108m3 for V , 5.00GPa for Pi , 1.01×105Pa for Pf , and 194GPa for B to find ΔV

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