Lecture 13 Notes: Heat Transfer and Specific Heat Capacity

Lecture 13 Notes

Date: February 20, 2026
Time: 9:12 AM
Topic: Heat Transfer and Specific Heat Capacity

Aktiv Warm Up

  • Chemical Reaction Balancing

    • Balance the following chemical equation:

    • {CH4} + {O2} \rightarrow {CO2} + {H2O}

  • Example Calculation:

    • When reacting 12 g of CH4 with excess O2 , calculate the moles of H_2O produced.

Heat Capacity and Specific Heat

  • Heat Capacity (C)

    • Defined as the energy needed to raise the temperature of a substance by 1 °C :

    • C = \frac{q}{\Delta T} , where q is heat energy and \Delta T is the change in temperature.

  • Specific Heat Capacity (c)

    • Defined as heat capacity per gram or mol of a substance.

    • Formula:

    • c = \frac{C}{m} , where m is the mass of the substance.

Comparison of Heats

  • Heat capacities of various substances:

    • Iron:

    • Heat capacity C = 20.8 ext{ J/°C} , specific heat c = 0.45 ext{ J/g°C}

    • Water:

    • Heat capacity C = 41.7 ext{ J/°C} , specific heat c = 4.18 ext{ J/g°C}

  • The energy required to raise the temperature varies by substance:

    • More mass (more "stuff") requires more energy to raise temperature (KE).

    • Higher heat capacity means harder to move, requiring more energy to raise temperature (KE).

Observational Patterns in Molar Specific Heats

  • Grouping substances by molar specific heat, formula, or phases reveals patterns:

    • Noble Gases:

    • Helium ( He ): c_m = 21 ext{ J/mol°C}

    • Neon ( Ne ): c_m = 21 ext{ J/mol°C}

    • Solids:

    • Aluminum ( Al ): c_m = 24 ext{ J/mol°C}

    • Liquids:

    • Water ( H2O ): cm = 50 ext{ J/mol°C}

    • Ionic Solids:

    • Sodium Chloride ( NaCl ): c_m = 50 ext{ J/mol°C}

    • Potassium Bromide ( KBr ): c_m = 52 ext{ J/mol°C}

  • Key Observations:

    • Metals exhibit similar molar specific heats.

    • Diatomic gases such as H2 and N2 require more energy to raise their temperature (higher specific heats).

    • Ionic solids have similar molar specific heats, larger molecules (like C8H{18} ) require more energy due to their complexity.

Specific Heat Capacity in Different States

  • The specific heat capacity in liquids and solids is influenced by bonding and intermolecular forces (IMFs).

    • When temperature increases, molecules move more vigorously (higher kinetic energy).

  • In gases, specific heat capacity depends on "degrees of freedom", which are:

    • Rotation

    • Vibration

    • Translation

  • Heat Energy Distribution Example:

    • For $9 of energy:$

    • 3 on rotations, 3 on vibrations, 3 on translations in a gas.

    • In gases, if heat energy only increases translations, the final temperature is higher.

  • Example:

    • c_m (He) = 21 ext{ J/mol°C}

Understanding Through Examples

  • Test Your Understanding 1:

    • Given two gas samples at 20 °C :

    • Sample A: 1 L ext{ of } CO_2

    • Sample B: 1 L ext{ of } CH3CH3

    • Energy Input: Adding 50 J to each sample, determine which sample will end up hotter.

Heat Transfer Calculations

  • When heat is transferred, it's described by the principle:

    • q_{ ext{input}} = C \Delta T

    • where C is heat capacity and \Delta T is change in temperature.

    • Rearranged, this can be used to calculate heat:

    • q = m c \Delta T

  • Illustrative Example:

    • Adding 250 J of heat to 10 ext{ g} of water at 10 °C where c = 4.18 ext{ J/g°C} determines the final temperature using:

    • 250 = 10 x 4.18 x (T_{ ext{final}} - 10)

    • Solving gives:

    • T_{ ext{final}} = 15.98 °C

Test Your Understanding 2

  • Problem: Adding 250 J of heat to 10 g of isopropanol at 10 °C , using c = 2.60 ext{ J/g°C} , find the final temperature:

    • 250 = 10 x 2.6 x (T_{ ext{final}} - 10)

  • Rearranged and solved gives final temperature of T_{ ext{final}} = 19 °C .

Nutrition Facts and Ratios

  • Example of using nutrition facts for calorimetry from a cookie recipe with:

    • Serving Size: 54 g

    • Calories: 171

    • Components include Total Fat, Saturated Fat, Cholesterol, and Sodium.

  • Ratios are crucial when calculating calories per batch (can scale recipe).

Calorimetry Principles

  • Heat exchange between the system and the surroundings, using the equation:

    • q{ ext{surr}} = -q{ ext{sys}}

  • The calorimeter measures heat exchanged:

    • q{ ext{water}} = m{ ext{water}} C{ ext{water}} \Delta T{ ext{water}}

    • q{ ext{metal}} = m{ ext{metal}} C{ ext{metal}} \Delta T{ ext{metal}}

    • Final temperatures should match to conserve energy in an isolated system.

  • Example Calculation of Metal's Specific Heat:

    • Given 100 g of water at 27 °C and 100 g of metal at 77 °C , with the water reaching 31.8 °C :

    • q_{ ext{water}} = 100 ext{ g} * 4.18 ext{ J/g°C} * (31.8°C - 27°C)

    • Rearranging gives specific heat of metal as:

    • C_{ ext{event}} = 0.44 ext{ J/g°C}

Changes in Kinetic Energy

  • Changes in heat transfer affect the kinetic energy (KE) of substances:

    • Changes are determined by both the amount of the substance and its specific heat capacity.

  • Relationship to the change in temperature:

    • \Delta KE = m c \Delta T