Page 545 - Algebra 1

Joint variation is found widely in scientific applications. An ideal gas can be characterized by three stated variables: absolute pressure P, volume V, and absolute temperature T. You can deduce the relationship between them from kinetic theory. This is called the ideal gas law. It is written as PV = nRT, where P is the absolute pressure in atmospheres, V is the volume of the vessel containing n moles of gas, n moles is the amount of substance of gas, R is the gas constant (0.08206), and T is the temperature in kelvins. Since R is a constant, the equation can be written as PV = 0.08206nT.
Use the ideal gas law to answer the questions.
9. What is the constant of variation in the ideal gas law equation?
10. How many moles of gas does it take to occupy 120 liters at a pressure of 2.3 atmospheres and a temperature of 340 K? Round the answer to the nearest tenth.
11. If a 50-liter container holds 45 moles of a gas at a temperature of 473.15 K, what is the pressure inside the container? Round the answer to the nearest tenth.
12. Generalize Solve the ideal gas law for the absolute pressure P.
An equation in several variables can be written in terms of one variable, as in the previous exercise. This will produce a quotient on one side of the equal sign in the equation. You can describe the variation in terms of a joint and an inverse variation.
13. Write State the ideal gas law solved for P in words using the phrases jointly proportional to and inversely proportional to.
By solving the ideal gas law for the absolute pressure P the equation
is written by as both a joint and an inverse variation. Many science applications involve more than one type of variation, as well as the square or square root of variable(s).
The load P in pounds that a horizontal beam can safely support varies jointly with the product of the width of the beam W in feet and the square of the depth D in feet, and inversely with the length L in feet.
14. Write an equation relating P, W, D, L, and a constant k.
15. How does P change when the length of the beam is doubled?
16. How does P change when the width and the depth of the beam are cut in half?
Caution
Sometimes there can be more than one type of variation in one situation. The type of variation depends on whether each variable is part of
a product or quotient within the equation of variation.
530 Saxon Algebra 1