Chemistry > Thermodynamics and Thermochemistry > 7.0 First Law of Thermodynamics

  Thermodynamics and Thermochemistry
    1.0 Introduction to Thermodynamics
    2.0 Thermodynamic Processes
    3.0 Heat $(Q)$
    4.0 Work $(W)$
    5.0 Internal Energy
    6.0 Zeroth Law of Thermodynamic
    7.0 First Law of Thermodynamics
    8.0 Heat Capacity
    9.0 Enthalpy $(H)$ or Heat Content
    10.0 Significance of $?H$ and $?E$
    11.0 Relationship Between $?H$ and $?E$
    12.0 Standard Enthalpy of Reaction
    13.0 Law of Thermodynamics
    14.0 Bond Energy or Bond Enthalpies
    15.0 Second Law of Thermodynamic
    16.0 Entropy (S)
    17.0 Spontaneous Processes
    18.0 Free Energy (G)
    19.0 Enthalpy, Entropy, Free Energy Changes and The Nature of Process
    20.0 Standard Free Energy Change
    21.0 Coupled Reactions
    22.0 Third Law of Thermodynamic
    23.0 Important Facts

7.2 Calculation of Work done $(W)$

For any expansion against external pressure ${p_{ext'.}}$


$W = - \int\limits_{{v_1}}^{{v_2}} {{P_{ext}}dv} $


Case 1: When V is constant (Isochoric process)

$W = 0,{\text{ }}{q_v} = \Delta E{\text{ }}$

Case 2: When ${P_{ext}}$ is constant (isobaric process)

$W = {\text{ }} - {\text{ }}{P_{ext}}{\text{ }}\Delta V{\text{ }} = {\text{ }}{q_p} = {\text{ }}\Delta E{\text{ }} + {\text{ }}{P_{ext}}{\text{ }}\Delta V$

If process is reversible and isobaric i.e. ${P_{ext}} = {P_{gas}} = {\text{constant}}$

$W = - {P_{ext}}{\text{ }}\Delta V = - {P_{gas}}{\text{ }}\Delta V{\text{ }}{q_p} = \Delta E + P\Delta V$

Case 3: When T is constant (Isothermal expansion)

Case (a): When the process is irreversible isothermal and ${P_{ext}}$ is constant.

$W = - {P_{ext}}{\text{ }}\Delta V$

Case (b): When the process is reversible and isothermal.

$W = - 2.303{\text{ }}nRT{\text{ }}{V_2}/{V_1} = - 2.303nRT{\text{ }}\log {P_1}/{P_2}$

Important Fact: During isothermal expansion for a sample of ideal gas $?E = 0$

Case 4: When $q = 0$ i.e. (adiabatic reversible process)


$W = \frac{{nR\left( {{T_2} - {T_1}} \right)}}{{\gamma - 1}} = \frac{{{P_2}{V_2} - {P_1}{V_1}}}{{\gamma - 1}}$

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