C10

Energy System and Surroundings

  • Definition: Energy exists everywhere in the universe and can be converted and transferred in various forms.

System vs. Surroundings

  • To analyze energy, one must define what constitutes the system and the surroundings.

  • System: An object or a defined set of objects for energy analysis.

    • Example: In a chemical reaction, a beaker with a chemical solution can be defined as the system.

  • Surroundings: All external factors outside the system.

    • For the beaker example, surroundings include the classroom, the podium, and everything else outside the solution.

  • Flexibility in Definition: The system can be defined in various ways (e.g., just the solution or the solution and the beaker together).

Forms of Energy

  • Focus on two forms of energy: Work and Heat.

Work

  • Definition: Work is the energy resulting from a force acting on an object over a distance.

    • Formula: Work ($W$) when done on the system is positive ($W > 0$).

  • If the surroundings do work on the system, the system gains energy.

  • If the system does work on the surroundings, the system loses energy (thus $W < 0$).

  • Key to solve problems involving work: Identify the sign based on whether the system or the surroundings are doing the work.

Heat

  • Definition: Heat is energy transferred due to temperature difference between system and surroundings.

    • Denoted as $q$.

  • If there's heat transfer from the surroundings to the system, $q$ is positive ($q > 0$).

    • Example: When heating a solution on a hot plate, the solution absorbs heat, hence $q$ is positive.

  • If the system releases heat to the surroundings, $q$ is negative ($q < 0$).

    • Example: A cooling hot plate releases heat; hence $q$ is negative.

  • Key to solve heat problems: Identify the sign based on absorption or release of energy.

Internal Energy

  • Definition: Denoted as $U$, internal energy is the sum of all forms of energy (kinetic, potential, etc.) in the system.

  • Measurement Difficulty: It’s hard to calculate absolute internal energy values, so only the change, denoted as $ riangle U$, is of interest.

  • Change of Internal Energy Calculation:

    • riangleU=U<em>final−U</em>initialriangle U = U<em>{final} - U</em>{initial}

    • Alternatively, can be expressed as:

    • riangleU=q+Wriangle U = q + W

    • Important: Identify signs for $q$ and $W$ before calculation.

Example Problem

  • Calculate the internal energy change for a system absorbing 100 calories of heat and doing 400 joules of work on surroundings.

    • Signs:

    • $q$ (positive, absorbed) = 100 calories

    • $W$ (negative, work done on surroundings) = -400 joules

    • Conversion needed: 1 calorie = 4.184 joules.

    • Therefore, 100 calories = 418.4 joules.

    • Substitute into equation:

    • riangleU=418.4extJ−400extJ=18.4extJriangle U = 418.4 ext{ J} - 400 ext{ J} = 18.4 ext{ J}

State Functions

  • Definition: State functions are properties that describe the current state of a system and are independent of the path taken to reach that state.

    • Example: Internal energy ($U$) is a state function. Controlled variables like temperature, pressure, and volume are also state functions.

  • Contrast with Heat and Work:

    • Heat and work are not state functions because they depend on the process (path) taken by the system rather than its current properties.

Calculating Work in Chemical Reactions

  • Most reactions occur under constant pressure (isobaric).

  • Work ($W$) is calculated using:

    • W=−PimesriangleVW = -P imes riangle V

    • Where $P$ = pressure, $ riangle V$ = change in volume.

  • Example of Chemical Reaction: When sodium bicarbonate reacts with hydrochloric acid, gas is produced, which expands the volume and does work on the surroundings.

Enthalpy

  • Definition: Denoted as $H$, enthalpy is another form of energy that accounts for internal energy, pressure, and volume.

    • Formula: H=U+PVH = U + PV

  • Change in Enthalpy ($ riangle H$): Focus is on changes due to reactions under constant pressure.

    • Since $H$ is a state function, $ riangle H$ can also be expressed as:

    • riangleH=QPriangle H = Q_P (heat absorbed at constant pressure).

Thermodynamic Processes

  • Endothermic Process: Absorbs heat; $q$ (or $ riangle H$) is positive.

  • Exothermic Process: Releases heat; $q$ (or $ riangle H$) is negative.

    • Example: Water evaporation (endothermic) $q = +40.67 ext{ kJ/mol}$.

    • Example: Water condensation (exothermic) $q = -40.67 ext{ kJ/mol}$.

Problem Evaluation of Enthalpy

  • Example: If a system releases 200 joules of heat while under constant pressure, it is exothermic as $q$ is negative.

  • Calculation of $ riangle H$ then follows from:

    • riangleH=QPriangle H = Q_P = negative value if losing heat.

Specific Heat

  • Definition: Specific heat ($c$) measures the heat required to change the temperature of a substance.

    • Different for air and water due to differences in energy required to raise temperature.

    • More energy is needed to increase water temperature compared to air, explaining perceived temperature differences in their presence.