Question

Prove that the change in internal energy is equal to the heat exchanged between the system and the surrounding.

Answer 1

"First law of thermodynamics":

The change in "internal energy" of a "closed system" will be equal to the "energy added to the system" "minus" the "work done" by the system on its surroundings.

${ \Delta E }_{ int }\quad =\quad Q\quad -\quad W$

This is the law of conservation of energy written in a form useful to systems involving heat transfer.

Internal energy:

Sum total of all potential and kinetic energies of a system. It is defined as the change during a process at constant volume. For irreversible expansion,

${ W }_{ rev }\quad =\quad -2.303\quad nRT\quad log\quad \frac { { V }_{ 2 } }{ { V }_{ 1 } } \\ For\quad internal\quad energy\quad ,\quad { W }_{ rev }\quad >\quad { W }_{ irrev }$

According to the "first law of thermodynamics", the "heat of the system" is "equal to" the "internal energy". The heat surrounding the system increases, so the heat of the system decreases because no heat is produced or destroyed."