Reading Atkins Elements of Physical Chemistry right now, and the book says: "At constant pressure and entropy, an increase in temperature ($\Delta T\gt0$) results in a decrease in $G_\mathrm m$ (molar Gibbs energy) ($\Delta G_\mathrm m\lt0$)." "At constant molar volume and temperature, an increase in pressure ($\Delta p >0$) results in an increase in molar Gibbs energy ($\Delta G_\mathrm m\gt0$)."
They have equations to describe this but I'm not really interested in the mathematical derivations (those are understandable) but rather in a logical, physical, and qualitative explanation of why these relations occur.
Given that $\Delta G$ indicates the maximum non-expansion work derivable from a system, what does this mean for the above relations? Does increasing the pressure of the system require work input ($\Delta G$ is positive) while increasing temperature result in the system doing work/an output of work ($\Delta G$ is negative)?
So, given a system (like a gas or something), why does $G$ change the way it does in response to $T$ and $p$ changes, and what does this physically mean for the system?
I'm a high school student (went through AP Chem) who's just trying to delve deeper into chemistry, so the simplest and most "layman's terms" explanation would probably help.