Page 91 - Physical Chemistry

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Chapter 2 because dV is an infinitesimal change and P is a finite change. If one term in an equa-
The First Law of Thermodynamics
tion contains a single change in a state function, then another term that contains only
state functions must contain a change. Thus, an equation cannot contain the expres-
sion PV V P or the expression PV VdP.
As to step 4, performing the calculations, errors can be minimized by carrying
units of all quantities as part of the calculation. Make sure you are using a self-
consistent set of units. Do not mix joules and kilojoules or joules and calories or joules
3
and cm atm in the same equation. If you are confused about what units to use, a strat-
egy that avoids errors is to express all quantities in SI units. Inconsistent use of units
is one of the most common student errors in physical chemistry.
Express your answer with the proper units. A numerical answer with no units is
meaningless.
In September 1999, the $125 million U.S. Mars Climate Orbiter spacecraft was lost. It
turned out that the engineers at Lockheed Martin sent data on the thrust of the spacecraft’s
thrusters to scientists at the Jet Propulsion Laboratory in units of pounds-force, but the JPL
scientists assumed the thrust was in units of newtons, and so their programming of rocket
firings to correct the trajectory produced an erroneous path that did not achieve orbit (New
York Times, Oct. 1, 1999, p. A1). You don’t have to be a rocket scientist to mess up on units.
On July 23, 1983, Air Canada Flight 143 ran out of fuel at 28,000 feet altitude and only
halfway to its destination. When the plane had been refueled in Ottawa, the plane’s on-board
fuel gauge was not working. Captain Robert Pearson knew that the plane needed 22,000 kg
of fuel for the trip. The fuel-truck gauge read in liters, so Pearson asked the mechanic for the
density of the fuel. He was told “1.77.” Pearson assumed this was 1.77 kg/L, and used this
figure to calculate the volume of the fuel needed. The plane was a new Boeing 767, and in
line with Canada’s conversion to metric units, its fuel load was measured in kilograms, in
contrast to older planes, which used pounds. The mechanic was used to dealing with fuel
loads in pounds (lb), so the figure of 1.77 he gave was actually 1.77 lb/L, which is 0.80 kg/L.
Because of this miscommunication due to omission of units, Pearson requested a bit less than
half the fuel volume he needed and took off with 22,000 pounds of fuel instead of 22,000 kg.
Although the plane was out of fuel, an emergency electric generator (the ram air tur-
bine) that uses the air stream resulting from the plane’s speed to supply power to the
plane’s hydraulic system gave Pearson some control of the plane. Also, emergency battery
power kept a few of the plane’s instrument-panel gauges working. Pearson was an experi-
enced glider pilot and flew the plane for 17 minutes after it ran out of fuel. He headed for
an abandoned Canadian Air Force base at Gimli. Approaching Gimli, he realized the plane
was coming in too high and too fast for a safe landing, so he executed a maneuver used
with gliders to lose speed and altitude; this maneuver had never been tried with a com-
mercial jet, but it worked. When the plane reached the runway, the crew saw people on the
runway—the abandoned runway was being used for car races. The crew used a backup
system to drop the landing gear; the nose wheel got stuck partway down and collapsed on
landing; the scraping of the nose along the ground, together with Pearson’s application of
the brakes, brought the plane to a stop before it reached the people on the runway. There
were no fatalities and only a few minor injuries when the passengers evacuated the plane.
Express the answer to the proper number of significant figures. Use a calcula-
tor with keys for exponentials and logarithms for calculations. After the calculation
is completed, it is a good idea to check the entire solution. If you are like most of
us, you are probably too lazy to do a complete check, but it takes only a few sec-
onds to check that the sign and the magnitude of the answer are physically reason-
able. Sign errors are especially common in thermodynamics, since most quantities
can be either positive or negative.
A solutions manual for problems in this textbook is available.