According to Boyle's Law, the pressure P (in kilopascals) exerted by a gas varies inversely as the volume V (in cubic decimeters) of a gas if the temperature remains constant. That is, PV clear Power A nuclear cooling tower is a hyperboloid, that is, a hyperbola rotated around its conjugate axis. Suppose the hyperbola used to generate the hyperboloid modeling the shape of the cooling tower has an eccentricity of
a. If the cooling tower is 150 feet wide at its narrowest point, determine an equation of the hyperbola used to generate the hyperboloid.
b. If the tower is 450 feet tall, the top is 100 feet above the center of the hyperbola, and the base is 350 feet below the center, what is the radius of the top and the base of the tower?c. Suppose the constant for oxygen at 25°C is 505.
a. Graph the function PV c for c 505.
b. Determine the volume of oxygen if the pressure is 101 kilopascals.
c. Determine the volume of oxygen if the pressure is 50.5 kilopascals. d. Study your results for parts b and c. If the pressure is halved, make a conjecture about the effect on the volume of gas.