Question

5. A tank with a cylindrical shape contains 4 ft' of water. If the temperature of the water changes from 40° F to 90° F, make use of Appendix B in the text to determine how much the volume of the water will change. Hint: the mass of the water does not change with temperature. (Ans: 0.0186 ft

Answer 1

Density of water at 40 degree F varsigma _40 degree = 1.940 slug 1 ft^3 or 62.424 pound/ft^3 Density of water at 90 degree F varsigma _90 degree = 62.118 pound/ft^3 Therefore Mass will remain same Let Initial volume V_1 = 14 ft^3 at 40 degree F Final volume V_2 = V_2 at 90 degree F Initial mass = final mass V_1 times varsigma _40 degree = V_2 times varsigma _90 degree 14 times 62.424 = 62.118 times V_2 V_2 = 14.0689 ft^3 V_2 = 14.067 ft^3 Therefore volume & water change = V_2 - V_1 = 14.067 - 14 = 0.067 ft^3 as we can see as the tempreature rises the volume of water Increases hence density decreases. & Mass & water remain constant