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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


  • 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 = T2T1

Change in internal energy, ΔU = U2U1

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

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

ΔU = U2U1 = Wad

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

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

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


  • 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”.


  • 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 = qv

    • At constant pressure:

  • ΔU = qppΔV

    (− pΔV) represents expansion work done by the system

    Or, U2U1 = qpp (V2V1)

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

  • Enthalpy (H) can be defined as

  • H = U + pV

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

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

  • At constant pressure, for finite changes:

  • ΔH = ΔU + pΔV

  • At constant pressure, ΔH = qp (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 = qv

  • Or, ΔH = ΔU = qv [ΔV = 0]

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

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

  • Thus, ΔH = ΔU + ΔngRT

  • 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…

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