Physical Chemistry Third Edition

2.3 Internal Energy: The First Law of Thermodynamics 57

wheremis the mass of the system,vcis the speed of its center of mass,zcis the vertical

coordinate of its center of mass, andgis the acceleration due to gravity.

Based on the experiments of Rumford, Mayer, Helmholtz, Joule, and many others

since the time of Joule, we now state thefirst law of thermodynamicsas it applies to a

system whose kinetic and potential energy do not change:For a closed system and for

any process that begins and ends with equilibrium states

∆Uq+w (2.3-2)

whereqis the amount of heat transferred to the system andwis the work done on the

system and where∆Uis the change in the value ofU,the internal energy, which is a

state function:

∆UU(final)−U(initial) (2.3-3)

In spite of the work of Rumford, Mayer, and Joule the credit for announcing the first
Hermann Ludwig von Helmholtz, law of thermodynamics went to Helmholtz.
1821 −1894, was a German physicist
and physiologist who studied the
energy of muscle contraction and who
was one of the first to propose that the
energy for all processes on the earth
ultimately came from solar radiation.

We accept the first law of thermodynamics as an experimentally established law

and accept the internal energy as a state function. This law is a version of the law of

conservation of energy, which is a general law of physics to which there are no known

exceptions. Apparent violations of energy conservation led particle physicists to search

for previously unknown particles that could be transferring energy to or from a system,

leading to the discovery of theneutrino.^2 Occasionally an unknown inventor in search

of gullible investors announces a machine that will produce more energy than it takes

in, violating the first law of thermodynamics. Such nonexistent machines are known

asperpetual motion machines of the first kind.

It is the total energy of a system that is governed by conservation of energy. The first

law of thermodynamics as stated in Eq. (2.3-2) applies to a closed system whose center

of mass is not accelerated and whose gravitational potential energy does not change.

If work is done to change the kinetic or potential energy of the system as a whole this

amount of work must be subtracted from the total work done to obtain the amount of

work that changes the internal energy.

The internal energy includes the rest-mass energy of the system. We always deal

only with energy changes or measure energy relative to some specified reference state

in order to avoid including the rest-mass energy in our calculations.

EXAMPLE2.13

Find the value of the rest-mass energy of 1.000 mol of argon gas, using Einstein’s equation,

Emc^2.

Solution

Erest-mass(0.039948 kg)(2. 9979 × 108 ms−^1 )^2  3. 5903 × 1015 J

(^2) E. Fermi,Z. Physik, 88 , 161 (1934).