CHAPTER 2 FIRST LAW OF THERMODYNAMICS 33
Thus, the change in internal energy is always proportional to the change
in temperature, and must be zero if there is no change in temperature.
If there is no temperature change the heat flow must exactly balance the
work:
For ΔT=0, ΔU=q+w=0 and q=−w (2.19)
Enthalpy
Most biological systems are open to the atmosphere, allowing the volume
to change in response to a change in energy. For this situation, heat
supplied to the system can change not only the internal energy of a sys-
tem but also result in a concurrent volume change. For example, if some
of the energy supplied as heat increases the volume of the system then
the change in internal energy will be smaller than found if the volume
did not change. For this reason, the heat supplied is equated to another
thermodynamic state function, called enthalpy. Formally, enthalpy, H, is
defined in terms of internal energy, U, and the product of pressure Pand
volume Vaccording to:
H=U+PV (2.20)
Biological systems are usually open to the atmosphere and so any pro-
cesses occur at a constant atmospheric pressure. In addition, the enthalpy
in most cases does not need to be considered as an absolute value but
only as a relative value, ΔH. Therefore, for most situations only the change
in enthalpy at constant pressure will be needed:
ΔH=ΔU+Δ(PV) =ΔU+PΔV (2.21)
Because enthalpy is defined in terms of state functions (internal energy,
pressure, and volume), enthalpy itself is also a state function. Therefore,
the change in enthalpy will be independent of the path between two states
and dependent only upon the initial and final states. The enthalpy term
is used because it alleviates the difficulty in relating the energy change
to the changes in other state functions. The change in internal energy is
given by heat minus work contribution, provided no other type of work
is performed. Substituting this into the expression for the enthalpy change
yields:
ΔH=ΔU+PΔV=(q−PΔV) +PΔV=q (2.22)
ΔU=q−pΔV (eqn 2.14)