Why is q positive in an isothermal expansion?

Question

Noah Aldrich · Accepted Answer

since it cannot expand without causing a temperature change if it does not flow into the system.

As the name suggests, an isothermal expansion is an increase in volume at a constant temperature.

Since the internal energy of an ideal gas depends only on temperature, the first law of thermodynamics is as follows:

#cancel(DeltaU)^(0) = q + w#

where #DeltaU# is the change in internal energy, #q# is heat flow, and #w# is work from the perspective of the SYSTEM.

Thus, #q = -w#. Since work is from the perspective of the SYSTEM, expansion work requires energy, and so, #w < 0#. As a result,

#-q < 0#

and that therefore means #q > 0#.

If it were a nonideal gas, it could expand not as easily (i.e. attractive intermolecular forces dominate), or it could expand too easily (i.e. repulsive intermolecular forces dominate). As a result, #DeltaU ne 0# for such a nonideal gas.

Cooper Anderson · Answer

undefined In an isothermal expansion, q is positive because heat is absorbed by the system from the surroundings, and the temperature remains constant.