Internal Energy

Whenever some process occurs, it is usually accompanied by some energy change. The energy may appear in different forms such as heat, light, work etc.

The evolution or absorption of energy in different processes clearly shows that every substance (or the system containing one or more substances) must be associated with some definite amount of energy, the actual value of which depends upon the nature of the substance and the conditions of temperature, pressure, volume and composition.

It is the sum of different types of energies associated with atoms and molecules such as electronic energy (E_e), nuclear energy (E_n), chemical bond energy (E_c), potential energy (E_p) and kinetic energy (E_k) which is further the sum of translational energy (E_t), vibrational energy (E_v) and rotational energy (E_r). It is usually represented by the symbol 'U' or 'E'.

Thus,

U or E = E_e + E_n +E_c +E_p + E_k + E_t + E_v + E_r

The energy thus stored within a substance (or a system) is called internal energy.

Sign of ∆U

Obviously, if U₁ > U₂ (or U_R> U_P), the extra energy possessed by the system in the initial state (or the reactants) would be given out and ∆U will be negative according to the above equations energy will be absorbed in the process and ∆U will be positive. Similarly, if U₁ <U2 (or U_P < U_R), energy will be absorbed in the process and ∆U will be positive. Hence, ∆U is negative if energy is evolved and ∆U is positive if energy is absorbed.

Units of U or E.

The units of energy are ergs (in CGS units) or joules (in SI units)

1 joule = 10⁷ ergs.

Problems

1. ∆E is always positive when

(a) System absorbs heat and work is done on it

(b) System emits heat and work is done on it

(c) System emits heat and no work is done on it

(d) System absorbs heat and work is done by it

Solution:

Heat absorbed increases the internal energy and also work done on a system increases the internal energy.