Physical Chemistry , 1st ed.

in potential energy to the water, which heats up. Assuming a mass of 25.0 kg

of water in the vat, what is the expected temperature change of the water?

The specific heat of water is 4.18 J/gK.

Solution

Using equation 2.1, we can calculate the work done on the water by the falling

weight:

work Fs(392 N)(2.00 m) 784 Nm 784 J

where we are using the fact that 1 joule 1 newton 1 meter. If all of this

work goes into heating the water, we get

784 J(25.0 kg)

1

1

00

k

0

g

g

(4.18 J/gK) T

T0.00750 K

This is not a large change in temperature. In fact, Joule had to drop the weight

many times before a detectable temperature change was noted.

2.3 Internal Energy and the First Law of Thermodynamics

Work and heat are manifestations of energy, but so far we have not discussed

energy directly. That will change here, and from now on energy and energy re-

lationships will be a major focus of our discussion of thermodynamics.

The total energy of a system is defined as the internal energy,symbolized

as U. The internal energy is composed of energy from different sources, like

chemical, electronic, nuclear, and kinetic energies. Because we cannot com-

pletely measure all types of energy in any system, the absolute total internal

energy of any system cannot be known. But all systems have some total en-

ergy U.

An isolated systemdoes not allow for passage of matter or energy into

or out of the system. (A closed system,on the other hand, allows for passage of

energy but not matter.) If energy cannot move in or out, then the total energy

Uof the system does not change. The explicit statement of this is considered

the first law of thermodynamics:

The first law of thermodynamics: For an isolated system,

the total energy of the system remains constant.

This does not mean that the system itself is static or unchanging. Something

may be occurring in the system, like a chemical reaction or the mixing of two

gases. But if the system is isolated, the total energy of the system does not

change.

There is a mathematical way of writing the first law, using the internal

energy:

For an isolated system,U 0 (2.10)

For an infinitesimal change, equation 2.10 can be written as dU0 instead.

The equation 2.10 statement of the first law has limited utility, because in

studying systems we usually allow matter or energy to pass to and from the sys-

tem and the surroundings. In particular, we are interested in energy changes of

the system. In all investigations of energy changes in systems, it has been found

32 CHAPTER 2 The First Law of Thermodynamics