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Consider a closed system which is comprised of a gas in a rigid vessel fitted with a
paddle wheel as shown in Fig. 1.10. If work is done on the gas by means of the paddle
wheel (process A), the temperature of the gas will rise. Then heat must be removed
from the gas (process B) in order to restore the gas to its initial state. During process A
there is work done but no heat transfer; during process B there is heat transferred but no
work done. During the complete cycle there is a net work input and a net heat transfer
from the system. Even relatively crude experiments with this apparatus show that as the
amount of work input is increased, the amount of heat that must be removed to restore
the system to its initial state increases proportionately.
Many experiments on systems as shown in Figs. 1.10 and on many other types of
systems indicate that, whenever a closed system executes a cycle, the net work output of
the system is proportional to the net heat input. This conclusion from experiments is
known as the first law of thermodynamics and is expressed by


 L   ;  L  J  , (1.40)
Q



Q

where J is a proportionality factor whose value depends only on the units selected
for W and Q.
The dimensions and possible units of work are obvious from the definition of work
given in Sec. H4. This is not the case with heat as defined in Sec.6, and one might infer
from that definition that suitable units might be devised in terms of numbers of standard
systems undergoing prescribed state changes. In fact, the early units of heat such as the
calorie and the British thermal unit (Btu, further abbreviated as B) were established in
just such a manner. On the basis of the experimental result given by Eq. 1.39, many
measurements were made of the proportionality factor which was called the
1
“mechanical equivalent of heat ,” often represented by the symbol J. For example, in SI
units, J = 4.186 J/ per calorie.
Since there is a fixed proportionality between
these units, one could be defined in terms of the
other. Or heat and work can be expressed in the
same units. Both can be measured in calories or
Joules, and heat as well as work can be measured
in Newton-meters. This is now done.
Consequently, J is simply a conversion factor.
Any equation expressing a physical relationship
must hold regardless of the system of units used
for the various quantities in the equation. The only
requirement is that the units used be consistent
and that the proper conversion factors be used in
any numerical calculation in order to make them

Fig.1-10 - One form of closed system

1
The mechanical equivalent of heat is that amount of work required to raise the temperature of a
substance of unit mass by 1 deg K
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