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 )

Step-by-step solution

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 10^5 ~Pa Change in volume ( dV )=-0.8 ~cm ^3 Bulk modulus (B)=2 10^9 ~Pa Now, B= -d P (d V / V) V=-B ( d V d P ) aligned & V=-2 10^9 (-0.8 10⁻⁶ ) 4 10^5 & =4 10⁻³ ~m ^3=4 litre aligned