Q.State the first law of thermodynamics.

Internal energy $U$ is the total energy stored in a system's constituent atoms, ions and molecules -- the sum of translational, vibrational, rotational, bond, electronic and intermolecular-interaction energy. Only its CHANGE, $\Delta U$, is ever measured or used; $U$ is what physically distinguishes structurally different forms of the same substance (graphite vs diamond, both pure carbon). Characteristics: it is extensive (scales with amount); it is a state function (depends only on $T,P,V,n$, never on path); $\Delta U_{cyclic}=0$; and $\Delta U=U_f-U_i$ comes out negative if the final state has lower energy, positive if higher.

The first law of thermodynamics -- the law of conservation of energy applied here -- states that the total energy of an isolated system stays constant however it converts between forms, giving the mathematical statement $\Delta U=q+w$, where $q$ is heat supplied TO the system and $w$ is work done ON it. Four everyday phrasings of the same law: energy disappearing as one type reappears as an equivalent amount of another; the total energy of system plus surroundings is conserved; energy is neither created nor destroyed, only converted; and heat and work are simply the two ways of changing a system's internal energy. Four special cases fall directly out of $\Delta U=q+w$: for a full CYCLE, $\Delta U=0$ so $q=-w$; at constant volume (ISOCHORIC), no expansion work is possible so $\Delta U=q_V$; for an ADIABATIC process, $q=0$ so $\Delta U=w$; and at constant pressure (ISOBARIC), $\Delta U=q-P\Delta V$ -- part of the absorbed heat does expansion work, the rest raises $U$.