How large a pressure increase (in ATM) must be applied to water if it is to be compressed in volume by 1.0%? The bulk modulus of water is 2.0 × 109 N/m2 and 1 ATM = 1.0 × 105 N/m2.
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3
Answer:
Given data:
The bulk modulus of water, K = 2 * 10⁹ N/m²
Volumetric strain = 1.0 % = 1 * 10⁻² = 10⁻²
To find: Pressure increase (in atm)
Solution:
We know,
Volumetric stress = Pressure increase
Let the required pressure increase be denoted as “dP”.
The formula for Bulk Modulus is given as,
K = [Volumetric Stress]/[Volumetric Strain]
⇒ K = dP / Volumetric strain
⇒ dP = K * Volumetric Strain
⇒ dP = [2 * 10⁹ N/m²] * [10⁻²]
⇒ dP = [2 * 10⁷] * [10⁻⁵] atm …… [given 1 atm = 1.0 * 10⁵ N/m²]
⇒ dP = 2 * 10² atm
⇒ dP = 200 atm
Thus, a pressure 200 atm must be applied to water if it is to be compressed in volume by 1.0%.
Answered by
0
Answer:
dP = 200 atm
Explanation:
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