Thermodynamics and Thermochemistry

Laws of Thermodynamics

Internal energy

• Internal energy (U) represents the total energy of a system (i.e., the sum of chemical, electrical, mechanical or any other type of energy).

• Internal energy of a system may change when:

  • Heat passes into or out of the system
  • Work is done on or by the system
  • Matter enters or leaves the system

Work

• For an adiabatic system which does not permit the transfer of heat through its boundary (shown in the figure), a change in its internal energy can be brought by doing some work on it.

• Initial state of the system, (1)

Temperature = T₁

Internal energy = U₁

• When some mechanical work is done, the new state (2) is obtained.

Temperature at state 2 = T₂

Internal energy at state 2 = U₂

• It is found that T₂ >T₁

Change in temperature, ΔT = T₂ − T₁

Change in internal energy, ΔU = U₂ − U₁

• The value of internal energy (U) is the characteristic of the state of a system.

• The adiabatic work (W_ad) required to bring about a change of state is equal to the change in internal energy.

ΔU = U₂ − U₁ = W_ad

• Thus, internal energy (U) of the system is a state function.

• When work is done on the system, W_ad = + ve

• When work is done by the system, W_ad = − ve

Heat

• Internal energy of the system can also be changed by transfer of heat from the surroundings to the system or vice versa, without doing any work.

• This exchange of energy, which is a result of temperature difference, is called heat (q).

• A system which allows heat transfer through its boundary is shown in the figure.

• At constant volume, when no work is done, the change in internal energy is, ΔU = q

• When heat is transferred from the surroundings to the system, q is positive.

• When heat is transferred from the system to the surroundings, q is negative.

General Case

• When change in state is brought about both by doing work (W) and by transfer of heat (q):

Change in internal energy, ΔU = q + W

• If W = 0 and q = 0 (i.e., no transfer of energy as heat or as work), then

ΔU = 0

This means that for an isolated system, ΔU = 0.

• ΔU = q + W, is the mathematical statement of the first law of thermodynamics.

• First law of thermodynamics states that “the energy of an isolated system is constant”.

Enthalpy

• We have ΔU = q + w (First law of thermodynamics)

• ΔU → Change in internal energy

  q → Heat absorbed by the system

  w → Work done

• • At constant volume:

• ΔU = q_v

• • At constant pressure:

• ΔU = q_p − pΔV

  (− pΔV) represents expansion work done by the system

  Or, U₂ − U₁ = q_p − p (V₂ − V₁)

  Or. q_p = (U₂ + pV₂) − (U₁ + pV₁) …(1)

• Enthalpy (H) can be defined as

• H = U + pV

• Thus, from equation (1) − q_p = H₂ − H₁ or, q_p = ΔH

• ΔH is independent of path, and hence, q_p is also independent of path.

• At constant pressure, for finite changes:

• ΔH = ΔU + pΔV

• At constant pressure, ΔH = q_p (heat absorbed by the system)

• ΔH is negative for exothermic reactions (which evolve heat during the reaction)

• ΔH is positive for endothermic reactions (which absorb heat from the surroundings)

• At constant volume: ΔU = q_v

• Or, ΔH = ΔU = q_v [ΔV = 0]

• For reactions involving gases, using ideal gas law, pΔV = Δn_gRT

• Δn_g = Number of moles of gaseous products − Number of moles of gaseous reactants

• Thus, ΔH = ΔU + Δn_gRT

• Extensive and Intensive Properties

• Extensive property: Value depends on the quantity or size of matter in the system

• Examples − mass, volume, internal energy, heat capacity, etc.

• Intensive property: Value does not depend on the quantity or size of matter in the system

• Examples − temperature, density, pressure, etc.

  Heat Capacity

• The increase in temperature (ΔT) is proportional to the heat transferred (q)

• q = coeff (C) × ΔT

  C → Heat capacity

• C is directly proportional to the amount of a substance.

• Molar heat capacity of a substance,, is the heat capacity of one mole of the substance.

• Molar heat capacity is also defined as the quantity of heat required to raise the temperature of one mole of a substance by one degree Celsius (or one Kelvin).

• Specific heat capacity c (o…