First law of thermodynamics for various processes

i. Isothermal process : Temperature is constant in such a process, so the internal energy is constant. Hence, $\Delta U = 0$. For an isothermal process,

The above equation implies that the heat absorbed by the system is entirely used for doing work on the surroundings. When work is done on the system by the surroundings, it results in the release of heat.

ii. Adiabatic process : In an adiabatic process there is no exchange of heat between the system and its surroundings, that is, $Q = 0$. Then

Thus an increase in the internal energy of the system is the work done on it. If the work is done by the system on the surroundings at the expense of its internal energy, the internal energy accompanying the adiabatic process would decrease.

iii. Isochoric process : Substitution of $W = -P_{ext}\,\Delta V$ into Eq. (4.12) gives

As the reaction is carried out in a closed container, the volume of the system is constant, or $\Delta V = 0$, and

Equation (4.17) shows that a change in internal energy of the system is due to heat transfer at constant volume. The subscript '$V$' indicates that heat is transferred at the constant volume. Further, $U$ being a state function, $Q_v$ is also a state function.

iv. Isobaric process : Usually chemical reactions are carried out in open containers under constant atmospheric pressure. In such reactions, $\Delta V \neq 0$. Writing the heat at constant pressure as $Q_p$, Eq. (4.16) reads $\Delta U = Q_p - P_{ext}\,\Delta V$; rearranging gives

$Q_p = \Delta U + P_{ext}\,\Delta V \qquad \text{...(4.18)}$ …