Question

Do the following problem by hand using TI30Xa calculator. Do the problem on a fresh sheet of paper (college ruled, printer paper or engineering paper). Find the decrease in pressure expected in an NFL football if it was inflated in a room at 80oF, left in the room for a while, and brought to field at 40oF, and left there for a while. Use the ideal gas law to find the decrease in pressure as a number in psi. The ideal gas law is given by
pv = RT where p is the pressure, v is the specific volume, R is the universal gas constant, and
T is the absolute temperature. If any numbers for variables are needed, go to your favorite internet source or books. You should seek the least numbers needed
**NOTE: Assume specific volume remains constant. If this is the case how will you solve the problem? What formulas you will use?

Answer 1

Given that the specific volume remains constant.

We know that ideal gas equation is PV = RT    ( for 1 mole of the gas )

Where

P = pressure : T = absolute temperature : R = gas constant : V = specific volume

Since V & R are constant    P T

For two case system   P / P' = T / T'

Where

P = initial pressure

P' = final pressure

T = initial temperature = 80 ^oF = 299.8 k

T' = final temperature = 40 ^oF = 277.6 K

Plug the values we get P / P' = T / T'

                                               = 299.8 / 277.6

                                               = 1.08

                                            P' = P / 1.08

                                                = 0.926 P

Therefore the final pressure = 0.926 times the initial pressure

So the decrease in pressure = P - P'

                                              = P - 0.926 P

                                              = 0.074 P

                              Therefore the decrease in pressure is 0.074 times the initial pressure