A sample of a liquid is kept at 1 atm. It is compressed to 5 atm, which leads to a change of volume of 0.8 cm³. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ______ litre. (Take 1 atm = 10⁵ Pa)

 

🔬 Bulk Modulus Concept – Find Initial Volume | Doubtify JEE

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📌 Question:

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm, which leads to a change of volume of 0.8 cm³.
If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ______ litre.
(Take 1 atm = 10⁵ Pa)

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🖼️ Question Image:

🧠 Concept & Formula Used:

Bulk Modulus (B) is defined as:

$$B = -\frac{\Delta P}{\Delta V / V} \Rightarrow \Delta V = \text{Change in Volume} \\ V = \text{Initial Volume}, \Delta P = \text{Final Pressure - Initial Pressure}$$

🔢 Step-by-Step Solution:

✅ Given:

• Initial pressure $P_1 = 1 \text{ atm}$, Final pressure $P_2=5\text{ atm}$

• $\Delta P = P_2 - P_1 = 4 \text{ atm} = 4 \times 10^5 \text{ Pa}$
  

• $\Delta V = 0.8 \, \text{cm}^3 = 0.8 \times 10^{-6} \, \text{m}^3$
  

• $B=2\text{GPa}=2\times {10}^9\text{Pa}$

✅ Apply Bulk Modulus Formula

$$B = \frac{\Delta P}{\Delta V / V} \Rightarrow 2 \times 10^9 = \frac{4 \times 10^5}{0.8 \times 10^{-6} / V}$$

✅ Solve for V

$$V = \frac{0.8 \times 10^{-6} \times 2 \times 10^9}{4 \times 10^5} = \frac{1.6 \times 10^3 \times 10^{-6}}{1} = 1.6 \times 10^{-3} \text{ m}^3 = 1.6 \, \text{litres}$$

✅ Final Answer:

Initial Volume = 1.6 litres

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🖼️ Solution Image:

🎥 Video Solution:

🧠 Pro Tip:

Bulk modulus questions often appear in Fluid Mechanics and are easy scoring topics if units and formulae are used correctly. Always:

• Convert atm to Pa

• Convert cm³ to m³

• Use absolute pressure difference $\Delta P$

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