Internal Energy and Enthalpy

Theory

Internal energy is the sum of all 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).

U = E_e + E_n + E_c + E_p + E_k

Change in internal energy can be when

• either work is done on or by the system.
• either heat is absorbed or released by the system.
• either matter enters or leaves the system.

The case in which a change of state is brought by doing work and transfer of heat,

Change in internal energy = heat absorbed + work done on the system

This gives the first law of thermodynamics:

Energy can neither be created nor be destroyed, although it may be changed from one form to another.

Pressure-volume work:

Work done when the gas expands or contracts against the external pressure (atmospheric pressure) is the pressure-volume work.

w = -PV

When the volume of a cylinder increases against a constant external pressure, V is positive and w is negative. So, as the volume of the cylinder expands, work is done on the surroundings by the system. Then the volume of a cylinder decreases under a constant external pressure, V is negative and w is positive. So, as the volume of the cylinder contracts, work is done on the system by the surroundings.

Free exapansion:

Expansion of a gas in vacuum (external pressure = 0) is called free expansion. No work is done whether the process is reversible or irreversible.

w_irrev = -p_exV = 0

We know that, U = q + w

For process at constant volume, U = q_v , where q_v is the heat supplied at constant volume.

Some important formulae:

Enthalpy:

Change in enthalpy (H) is a measure of heat evolved or absorbed in a reaction or process at constant temperature and constant pressure.

H = q_p = U + pV

When H is negative, then reaction is exothermic, i.e. evolving heat.

When H is positive, then reaction is endothermic, i.e. absorbing heat.

At constant volume, Î”V = 0, then Î”H = Î”U = qv

So, q_p = q_v + pV

or q_p = q_v +n_gRT

where n_g represents number of moles of gaseous products minus the number of moles of gaseous reactants.