A moonshiner produces pure ethanol (ethyl alcohol) late at night and stores it in a stainless steel tank in the form of a cylinder 0.300 m in diameter with a tight-fitting piston at the top. The total volume of the tank is 250 L(0.250 m3). In an attempt to squeeze a little more into the tank, the moonshiner piles 1420 kg of lead bricks on top of the piston. What additional volume of ethanol can the moonshiner squeeze into the tank? (Assume that the wall of the tank is perfectly rigid.)

Solution 95P Step 1: Diameter of the tank, d =0.3m So radius , r =0.153 3 Volume of the tank , v=0.250m F mg Pressure , p= A = A ………….(1) Area of the tank, A = r A = × ( 0.15 )2 A =3.14 × 0.0225 A =0.07065 Put this value in ( 1 ) dp= 1420×9.8 0.07065 dp=1.96970 ×10 5 Step 2: The bulk modulus ( The relative change in the volume of a body produced by a unit compressive or tensile stress acting uniformly over its surface ) is given by the formula. dp K = -v dv dp K = - (dv/v)