Question

The compressibility of a liquid is 4 x 10-8 N-1 m2. If 2 litre of liquid is subjected to extra pressure of 2 x 106 N/m?, then the decrease in volume of the liquid will be 1.414 cc 421 CC 160 CC 3.69 CC​

Answer 1

Given :

compressibility of a liquid, K = 4 x 10-8 N-1 m2

Extra pressure, P = 2 x 106 N/m .

Volume, V = 2L .

Find: Decrease in volume of the liquid. (∆V)

Solution :

• In this question we have given the compressibility of the liquid and the extra pressure that is applied on 2L liquid also given .

• We have to find the decrease in volume of the liquid . For this we have to apply the formula of bulk modulus , as it is inversely proportional to the compressibility .

• Bulk modulus is defined as the" measure of the ability of a substance to withstand changes in volume when under compression on all sides ".

• The formula of bulk modulus is B = -P/∆V/V.

• compressibility K = 1/B = -∆V/PV

• Minus sign represents increase in pressure and decrease in volume.

∆V = KPV

= 4*10-⁸ * 2*10⁶ * 2

= 16 * 10-² litre

= 16* 10-² * 10³ cm³

= 160 cc .

• Therefore, Decrease in volume of the liquid will be 160 cc .