Answer :
Answer:
[tex]\dfrac{\Delta V}{V_0}=8.1\times 10^{-7}[/tex]
Explanation:
Given that
Bulk modulus ,K= 7.1 x 10¹⁰ N/m²
Initial pressure ,P ₁= 0.568 x 10⁵ N/m² ( 1 Pa = 1 N/m²)
Final pressure ,P₂ = 0 Pa
We know that bulk modulus given as
[tex]K=\dfrac{\Delta P}{\dfrac{\Delta V}{V_0}}[/tex]
[tex]\dfrac{\Delta V}{V_0}=\dfrac{\Delta P}{K}[/tex]
ΔV=Change in the volume
[tex]\dfrac{\Delta V}{V_0}=\dfrac{0.568\times 10^5}{7.1\times 10^{10}}[/tex]
[tex]\dfrac{\Delta V}{V_0}=8.1\times 10^{-7}[/tex]
Therefore the fractional change in the volume
[tex]\dfrac{\Delta V}{V_0}=8.1\times 10^{-7}[/tex]
The required fractional change is,
[tex]\delta(\frac{ V}{V_0}) =-8\times 10^{-5}[/tex]
Bulk Modulus:
The bulk modulus of elasticity is one of the measures of the mechanical properties of solids.
Other elastic modules include Young’s modulus and Shear modulus. In any case, the bulk elastic properties of a material are used to determine how much it will compress under a given amount of external pressure. Here it is important to find and note the ratio of the change in pressure to the fractional volume compression.
And it is represented by,
[tex]B=\frac{\Delta P}{(\frac{\Delta V}{V} )}[/tex]
Given that,
Bulk Modulus (K) = [tex]7.1 \times 10^{10} N/m^2\\[/tex]
delta (P)=[tex]0.568 \times105 Pa[/tex]
Now if we take,[tex]K=-V_0(\frac{\delta p}{\delta v} )[/tex] then,
[tex]\delta(\frac{ V}{V_0})=-\frac{\delta P}{K}\\ =\frac{-0.568\times 10^5}{7.1\times 10^{10}} \\\delta(\frac{ V}{V_0}) =-8\times 10^{-5}[/tex]
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