We are now equipped to deal with the changes that occur when a perfect gas expands
adiabatically. A decrease in temperature should be expected: because work is done but
no heat enters the system, the internal energy falls, and therefore the temperature of
the working gas also falls. In molecular terms, the kinetic energy of the molecules falls
as work is done, so their average speed decreases, and hence the temperature falls.
The change in internal energy of a perfect gas when the temperature is changed
from Ti to Tf and the volume is changed from Vi to Vf can be expressed as the sum of
two steps (Fig. 2.17). In the first step, only the volume changes and the temperature is
held constant at its initial value. However, because the internal energy of a perfect gas
is independent of the volume the molecules occupy, the overall change in internal
energy arises solely from the second step, the change in temperature at constant
volume. Provided the heat capacity is independent of temperature, this change is.
We are now equipped to deal with the changes that occur when a perfect gas expandsadiabatically. A decrease in temperature should be expected: because work is done butno heat enters the system, the internal energy falls, and therefore the temperature ofthe working gas also falls. In molecular terms, the kinetic energy of the molecules fallsas work is done, so their average speed decreases, and hence the temperature falls.The change in internal energy of a perfect gas when the temperature is changedfrom Ti to Tf and the volume is changed from Vi to Vf can be expressed as the sum oftwo steps (Fig. 2.17). In the first step, only the volume changes and the temperature isheld constant at its initial value. However, because the internal energy of a perfect gasis independent of the volume the molecules occupy, the overall change in internalenergy arises solely from the second step, the change in temperature at constantvolume. Provided the heat capacity is independent of temperature, this change is.
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