Question

What is the role of potential energy in changing a system from one state to another?

Answer 1

Thermodynamics first law says energy is always conserved:

energy of a system + surroundings at state 1 = energy of a system + surroundings at state 2

now the role of potential energy can come into play when we talk about taking anyting from higher to lower state(potential energy decreases) or lower to higher height(potential energy increeases).

for example:

if you drop a pebble from a top of roof, the potential energy is = mgh

m= mass of pebble

g= gravity

h = height of roof

now when it reaches the ground potential energy = mgh = 0 ,as h= 0

here all the potential energy is converted to kinetic energy just before it hits the ground

mgh = 1/2 m v²

so potential energy essentially deals with height ,so if it is changing from one state to another,the energy increases or decreases as explained above.