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Physics Question 48 – JEE-MAIN 2025

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A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to 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)

The bulk modulus quantifies a substance's resistance to compression and is defined as the ratio of pressure change to the fractional volume change.

Step 1: Calculate Change in Pressure and Convert Units✦ Active

The initial pressure is P1=1 atm and the final pressure is P2=5 atm. The change in pressure is ΔP=P2−P1=5 atm−1 atm=4 atm. Convert this to Pascals using 1 atm=105 Pa:

ΔP=4×105 Pa

The bulk modulus is B=2 GPa. Convert this to Pascals using 1 GPa=109 Pa:

B=2×109 Pa

The change in volume is ΔV=0.8 cm3. Convert this to cubic meters:

|ΔV|=0.8 cm3=0.8×(10−2 m)3=0.8×10−6 m3
Step 2: Apply Bulk Modulus Formula to Find Initial Volume○ Expand

The bulk modulus is defined as B=−VΔPΔV. Since ΔV is a decrease, we use its magnitude. Rearranging for initial volume V:

V=B|ΔV|ΔP

Substitute the converted values:

V=(2×109 Pa)×0.8×10−6 m34×105 Pa

Calculate the initial volume:

V=2×0.84×109−6−5 m3=0.4×10−2 m3=4×10−3 m3
💡 Teacher's Secret Hint

Ensure all units are consistent (SI units are recommended) before performing calculations to avoid errors.

Step 3: Convert Volume to Litres○ Expand

The question asks for the initial volume in litres. Use the conversion factor 1 m3=1000 litres:

V=4×10−3 m3×1000 litres1 m3=4×10−3×103 litres=4 litres
💡 Teacher's Secret Hint

Always double-check the required units for the final answer and perform the necessary conversions.

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