3.3 Heat Exchange and the First Law of Thermodynamics
A temperature increase from 14.5 to 15.5 °C in one gram of water at constant
atmospheric pressure can be a result of the absorption of heat (Chap. 2), or a result
of adiabatic work (Sect. 3.2)—or some combination of work and heat.
Consider again the system in Sect. 3.2. Imagine that we already compiled the
internal energy database of the system. Now, we perform a different kind of
experiment on the same system: In this new experiment, the system is not thermally
insulated in its change i ! f, during which the system may interact with its surroundings in both work, W, and heat exchange, Q. Suppose that the resulting work
(the nonadiabatic work W i!f which is not necessarily equal to U f – U i ) is determined experimentally. There are two ways to consider the heat exchange, Q.
It can be determined by using an available calorimetric experimental apparatus.
The result (Q i!f ) calorie ,
Àm water c p;water DT ¼ Q i!f
À
Á
calorie
ð19Þ
is expressed in the unit of calorie, where DT is the temperature rise in the calorimetric substance of water, as it was described in Chap. 2, Eq. (11A).
At the same time, the supposition of “the conservation of energy” suggests that
heat exchange is quantitatively balanced with the difference between the internal
energy change of the system and the (general) work exchange of the system. That
is, one can define a theoretical Q i!f (based on the conservation supposition) in the
unit of joule as
U f À U i
À
Á À ÀW i!f
À
Á Q i!f
ð20Þ
If the supposition is correct, an equivalent relationship must exists between the
theoretical Q i!f in (20) and the calorimetric Q i!f
À
Á
calorie
.
Note that the theoretical Q i!f and the calorimetric Q i!f
À
Á
calorie
are measured in
terms of different units – the unit of joule and the unit of calorie, respectively. It is,
therefore, necessary to introduce a conversion factor J in the expression of the
equivalent relation
Q i!f ¼ J Q i!f
À
Á
calorie
or
U f À U i
À
Á þ W i!f ¼ J Q i!f
À
Á
calorie
(The equation is reducible to Eq. (17) in the limit of Q ! 0.) Imagine that
experiments of the kind were repeatedly carried out along different paths with
different works and heat. Joule and others obtained experimental outcomes showing
that in all cases the conversion factor J’s are found to be the same constant, i.e., a
42
3 The First Law: The Production of Heat …
A temperature increase from 14.5 to 15.5 °C in one gram of water at constant
atmospheric pressure can be a result of the absorption of heat (Chap. 2), or a result
of adiabatic work (Sect. 3.2)—or some combination of work and heat.
Consider again the system in Sect. 3.2. Imagine that we already compiled the
internal energy database of the system. Now, we perform a different kind of
experiment on the same system: In this new experiment, the system is not thermally
insulated in its change i ! f, during which the system may interact with its surroundings in both work, W, and heat exchange, Q. Suppose that the resulting work
(the nonadiabatic work W i!f which is not necessarily equal to U f – U i ) is determined experimentally. There are two ways to consider the heat exchange, Q.
It can be determined by using an available calorimetric experimental apparatus.
The result (Q i!f ) calorie ,
Àm water c p;water DT ¼ Q i!f
À
Á
calorie
ð19Þ
is expressed in the unit of calorie, where DT is the temperature rise in the calorimetric substance of water, as it was described in Chap. 2, Eq. (11A).
At the same time, the supposition of “the conservation of energy” suggests that
heat exchange is quantitatively balanced with the difference between the internal
energy change of the system and the (general) work exchange of the system. That
is, one can define a theoretical Q i!f (based on the conservation supposition) in the
unit of joule as
U f À U i
À
Á À ÀW i!f
À
Á Q i!f
ð20Þ
If the supposition is correct, an equivalent relationship must exists between the
theoretical Q i!f in (20) and the calorimetric Q i!f
À
Á
calorie
.
Note that the theoretical Q i!f and the calorimetric Q i!f
À
Á
calorie
are measured in
terms of different units – the unit of joule and the unit of calorie, respectively. It is,
therefore, necessary to introduce a conversion factor J in the expression of the
equivalent relation
Q i!f ¼ J Q i!f
À
Á
calorie
or
U f À U i
À
Á þ W i!f ¼ J Q i!f
À
Á
calorie
(The equation is reducible to Eq. (17) in the limit of Q ! 0.) Imagine that
experiments of the kind were repeatedly carried out along different paths with
different works and heat. Joule and others obtained experimental outcomes showing
that in all cases the conversion factor J’s are found to be the same constant, i.e., a
42
3 The First Law: The Production of Heat …