scan_pschlax_2025-01-22-12-01-09 (2)

Page 1: First Law of Thermodynamics

• Quiz Information

  • Quiz scheduled for Friday from 2:00-3:30

• First Law of Thermodynamics

  • Equation: ( \Delta U = q + w )

  • ( \Delta U ): Change in internal energy of a closed system (cannot exchange matter with surroundings)

  • Energy changes occur via work (w) and/or heat (q) exchange with surroundings

• Heat (q)

  • Form of energy involving microscopic collisions among particles

  • Energy transfer occurs when one particle interacts with another

• Ideal Gases

  • Types:

    • Isothermal: Temperature remains constant

    • Isobaric: Pressure remains constant

• Equations for Ideal Gases

  • For monoatomic ideal gases: ( \Delta U = \frac{3}{2} n R \Delta T )

  • Work done in isothermal process: ( w = -P \Delta V )

  • Work during isobaric process: ( w = -\Delta U )

Page 2: Chemical Reactions and Enthalpy

• Chemical Reactions

  • Typically occur at constant pressure (P), but not always

• Enthalpy (H)

  • Defined as a state function: ( H = U + PV )

  • Change in Enthalpy (( \Delta H )) relates to heat exchange:

    • ( \Delta H = q_p )

    • Where ( q_p ): Heat measured at constant pressure

• Types of Reactions

  • Exothermic: Heat is released to the surroundings (( \Delta H < 0 ))

  • Endothermic: Heat is absorbed from the surroundings (( \Delta H > 0 ))

Page 3: Heat Capacity

• Heat Capacity (C)

  • For ideal monoatomic gases: ( C_v = \frac{3}{2} R ) and ( C_p = \frac{5}{2} R )

  • Specific Heat: Energy needed to raise the temperature of 1g of a substance by 1°C

  • Specific heat of water: 4.184 J/g°C

• Isobaric Processes

  • Relation: ( q = \Delta U + P \Delta V )

  • At constant volume calorimetry: ( q_u = \Delta U )

Page 4: Molar Heat Capacity

• Molar Heat Capacity (C_v)

  • Defined as the energy needed to raise the temperature of 1 mole of a substance by 1°C at constant volume

  • Takes into account all molecular motions: translation, rotation, vibration, and non-covalent attractions

  • Typically, larger molecules with stronger internal forces exhibit higher ( C_v ) values

• General Relation

  • Relation between heat capacities:

    • ( n C_p = n C_v + R )

  • Usually defined experimentally

Page 5: Example Reaction and Energy Release

• Chemical Reaction

  • Example: ( C_6H_{12}O_6 (s) + 6 O_2 (g) \rightarrow 6 CO_2 (g) + 6 H_2O (l) )

  • Energy released: -2800 kJ/mol at 298 K

• Stoichiometry

  • For 1 mole of glucose, produces 6 moles of CO2

  • Energy release for 1.5 moles of CO2 burned: [ \Delta H = 1.5 \text{ moles} \times (-2800 ext{ kJ}) = -4200 ext{ kJ} ]

Page 6: Calorimetry and Heat Measurement

• Calorimetry in Reactions

  • When reaction releases heat, calorimeter absorbs that heat

• Heat Measurement

  • Using water as a medium:

    • ( q_{cal} = T_{final} - T_{initial} )

  • Example: Using water with specific heat

    • ( 100g \times 4.184 ext{ J/g°C} ) for heat capacity

• Endothermic vs Exothermic Reactions

  • Involves temperature changes (( \Delta T )) in calorimetric measurements