2.3 Internal Energy: The First Law of Thermodynamics
57
where m is the mass of the system, v c is the speed of its center of mass, z c is the vertical
coordinate of its center of mass, and g is 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 the first law of thermodynamics as 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
∆U q + w
(2.3-2)
where q is the amount of heat transferred to the system and w is the work done on the
system and where ∆U is the change in the value of U, the internal energy, which is a
state function:
∆U U(final) − U(initial)
(2.3-3)
In spite of the work of Rumford, Mayer, and Joule the credit for announcing the first
law of thermodynamics went to Helmholtz.
Hermann Ludwig von 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 the neutrino. 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
as perpetual 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.
E X A M P L E 2.13
Find the value of the rest-mass energy of 1.000 mol of argon gas, using Einstein’s equation,
E mc 2 .
Solution
E rest-mass (0.039948 kg)(2.9979 × 10 8 m s −1 ) 2 3.5903 × 10 15 J
2 E. Fermi, Z. Physik, 88, 161 (1934).
57
where m is the mass of the system, v c is the speed of its center of mass, z c is the vertical
coordinate of its center of mass, and g is 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 the first law of thermodynamics as 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
∆U q + w
(2.3-2)
where q is the amount of heat transferred to the system and w is the work done on the
system and where ∆U is the change in the value of U, the internal energy, which is a
state function:
∆U U(final) − U(initial)
(2.3-3)
In spite of the work of Rumford, Mayer, and Joule the credit for announcing the first
law of thermodynamics went to Helmholtz.
Hermann Ludwig von 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 the neutrino. 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
as perpetual 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.
E X A M P L E 2.13
Find the value of the rest-mass energy of 1.000 mol of argon gas, using Einstein’s equation,
E mc 2 .
Solution
E rest-mass (0.039948 kg)(2.9979 × 10 8 m s −1 ) 2 3.5903 × 10 15 J
2 E. Fermi, Z. Physik, 88, 161 (1934).