Many coronal heating mechanisms have been suggested to balance the los
ses from this tenuous medium by radiation, conduction, and plasma mass
Bows. A previous paper (Walsh, Bell, and Hood, 1995) considered a tim
e-dependent heating supply where the plasma evolved isobarically along
the loop length. The validity of this assumption is investigated by i
ncluding the inertial terms in the fluid equations making it necessary
to track the sound waves propagating in a coronal loop structure due
to changes in the heating rate with time. It is found that the tempera
ture changes along the loop are mainly governed by the variations in t
he heating so that the thermal evolution can be approximated to a high
degree by the simple isobaric case. A typical isobaric evolution of t
he plasma properties is reproduced when the acoustic time scale is sho
rt enough. However, the cooling of a hot temperature equilibrium to a
cool one creates supersonic flows which are not allowed for in this mo
del.