What is the bulk modulus of a material if a pressure increase of 1000 kPa results in a volume decrease of 0.01 m³ for a volume of 1 m³? (2022)

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Q: What is the bulk modulus of a material if a pressure increase of 1000 kPa results in a volume decrease of 0.01 m³ for a volume of 1 m³? (2022)

Solution: Bulk modulus (K) = -ΔP / (ΔV/V) = 1000 kPa / (0.01 m³ / 1 m³) = 100000 kPa.

Steps: 7

Step 1: Identify the change in pressure (ΔP). In this case, ΔP = 1000 kPa.
Step 2: Identify the change in volume (ΔV). Here, ΔV = -0.01 m³ (it's negative because the volume decreases).
Step 3: Identify the original volume (V). The original volume is V = 1 m³.
Step 4: Calculate the ratio of the change in volume to the original volume (ΔV/V). This is ΔV/V = -0.01 m³ / 1 m³ = -0.01.
Step 5: Use the formula for bulk modulus (K): K = -ΔP / (ΔV/V).
Step 6: Substitute the values into the formula: K = -1000 kPa / (-0.01).
Step 7: Calculate the bulk modulus: K = 1000 kPa / 0.01 = 100000 kPa.