# Same temperature and entropy

by Antonio2090
Tags: entropy, temperature
 P: 1 Does entropy change when temperature remains constant? What if heat is added into a system, while the volume expands and the pressure drops at a constant temperature? Is there any change in entropy?
 Sci Advisor HW Helper PF Gold P: 2,532 Does entropy change when temperature remains constant? Yes, entropy can change even at constant temperature. For example, adding material into a system increases entropy, as does any irreversible isothermal process such as free expansion of a gas into a vacuum. What if heat is added into a system, while the volume expands and the pressure drops at a constant temperature? Is there any change in entropy? Yes, heating a system always increases its entropy. Another way to view this process is that the temperature is the same, but the space for atomic motion has increased because the volume increased. There are therefore more available microstates for the system, which is equivalent to saying the entropy has increased.
$$\Delta G = \Delta H - T\Delta S$$
G is the Gibbs free energy, H the enthalpy, T temeprature, S entropy. There are lots of processes that use this relationship: phase transitions, chemical reactions, etc. The sign of $$\Delta G$$ tells you if the processes is spontaneous or not- in biochemical reactions, non-spontaneous reactions are generally powered by using the chemical energy in adenosine triphosphate (ATP) or guanine triphosphate (GTP)- but not in the way elementary texts describe.