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 . If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ______ litre. (Take 1 atm = 1Pa) [2025]

Question

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 ${cm}^{3}$ . If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ______ litre. (Take 1 atm = $10^{5}$ Pa) [2025]

Smart Achievers · Accepted Answer

(4)

Given, Initial pressure of liquid ( $P_{i}$ ) = 1 atm Final pressure of liquid ( $P_{f}$ ) = 5 atm.

Change in pressure (dP) = $P_{f} - P_{i} =$ 4 atm = $4 \times 10^{5} Pa$

Change in volume (dV) = – 0.8 ${cm}^{3}$

Bulk modulus (B) = $2 \times 10^{9} Pa$

Now, $B = \frac{- d P}{(d V / V)} \Rightarrow V = - B (\frac{d V}{d P})$

$\Rightarrow V = - 2 \times 10^{9} \times \frac{(- 0.8 \times 10^{- 6})}{4 \times 10^{5}}$

$= 4 \times 10^{- 3} m^{3} = 4 litre$

Solution

Q.
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 ${cm}^{3}$ . If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ______ litre. (Take 1 atm = $10^{5}$ Pa) [2025]

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Solution

Q. 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 = 105Pa) [2025]

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Q.
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 ${cm}^{3}$ . If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ______ litre. (Take 1 atm = $10^{5}$ Pa) [2025]