What is the bulk modulus of a material if a pressure increase of 1000 kPa causes

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

Options:

Correct Answer: 10000 kPa

Exam Year: 2022

Solution:

Bulk modulus (K) = -ΔP / (ΔV/V) = 1000 kPa / (0.01 m³ / 1 m³) = 100000 kPa = 10000 kPa.

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

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

Step 1: Understand the formula for bulk modulus (K), which is K = -ΔP / (ΔV/V). Here, ΔP is the change in pressure, ΔV is the change in volume, and V is the original volume.
Step 2: Identify the values given in the question. We have ΔP = 1000 kPa, ΔV = -0.01 m³ (since the volume decreases), and V = 1 m³.
Step 3: Calculate the ratio ΔV/V. This is done by dividing the change in volume (ΔV) by the original volume (V). So, ΔV/V = -0.01 m³ / 1 m³ = -0.01.
Step 4: Substitute the values into the bulk modulus formula. We have K = -ΔP / (ΔV/V) = -1000 kPa / -0.01.
Step 5: Simplify the calculation. K = 1000 kPa / 0.01 = 100000 kPa.
Step 6: Write the final answer. The bulk modulus of the material is 100000 kPa.

Bulk Modulus – The bulk modulus is a measure of a material's resistance to uniform compression, defined as the ratio of pressure increase to the relative decrease in volume.