Exmple: Mathematics as Language

The following section is an excerpt from the example laboratory report, titled Proper Inflation of a Basketball. (The entire example report is available in either  Microsoft Word Format for printing, or  HTML format for online viewing.)

It is important to realize that the number of strokes needed to properly inflate the basketball is valid only for the particular pump that we have used. The important quantity is the pressure of the air that is in the ball. Fortunately, we can use the ideal gas law to determine the pressure in the ball from our measurements. The ideal gas law states that (Serway, 1997, p. 542)
 
(2)
where P is the pressure of an amount of gas, V is the volume the gas occupies, n is the number of molecules in this amount of gas, T is the temperature of the gas, and k is Boltzmann's constant. In SI units, k = 1.38 ´ 10- 23 J/K (Serway, 1997, p. 542). In this equation, the temperature is measured on the absolute scale of degrees Kelvin or K.

When we use a pump to inflate a basketball, we take a fixed number of air molecules, n, initially at room temperature and pressure, and squeeze them into a smaller volume. Although the process of compressing the gas heats it, it quickly looses this heat and returns to room temperature. Since n and T in Equation (2) are constants, we can rewrite this equation as
 
(3)
where the subscripts "1" and "2" refer to the initial and final conditions of the gas. Here, the initial pressure of the gas is atmospheric pressure at room temperature, Patm. The initial volume of the gas is the volume of the basketball, Vball, and N times the volume of the pump, Vpump. Recall that N is the number of strokes of the pump we used to inflate the ball.

Note what's here:

Note what's missing: