Chapter 7: Energy, Heat, and Thermodynamics in Chemistry

Energy and Work

Definitions and Concepts

Energy is a fundamental concept in chemistry, representing the capacity to do work. Work is defined as the result of a force acting through a distance, such as pushing a box across the floor. Energy can be transferred between objects through work or heat.

• Energy: Capacity to do work.

• Work: Result of a force acting through a distance.

• Heat: Flow of energy caused by a temperature difference.

• Objects exchange energy through heat and work.

Types of Energy

• Kinetic energy: Energy associated with the motion of an object.

• Thermal energy: Energy associated with the temperature of an object.

• Potential energy: Energy associated with the position or composition of an object.

• Chemical energy: Energy associated with the relative positions of electrons and nuclei in atoms and molecules; a form of potential energy.

Law of Conservation of Energy

Fundamental Principle

The law of conservation of energy states that energy can neither be created nor destroyed. However, energy can be transferred from one object to another.

• System: The part of the universe being studied.

• Surroundings: Everything outside the system.

Units of Energy

Measurement and Conversion

Energy is measured in various units, with the joule (J) being the SI unit. Other common units include the calorie and kilojoule.

• Kinetic energy equation: $KE = \frac{1}{2}mv^2$

• Joule (J): $1 \text{J} = 1 \text{kg} \cdot \text{m}^2/\text{s}^2$

• Kilojoule (kJ): $1 \text{kJ} = 1000 \text{J}$

• Calorie (cal): $1 \text{cal} = 4.184 \text{J}$

• Calorie (Cal): $1 \text{Cal} = 1000 \text{cal}$ (nutritional calorie)

First Law of Thermodynamics

Internal Energy and State Functions

The first law of thermodynamics states that the total energy of the universe is constant. Internal energy (E) of a system is the sum of the kinetic and potential energies of its particles. Internal energy is a state function, meaning its value depends only on the state of the system, not the path taken to reach that state.

• State function: Property dependent only on the current state, not the process.

• Change in internal energy: $\Delta E = E_{\text{final}} - E_{\text{initial}}$

• For a chemical system: $\Delta E = E_{\text{products}} - E_{\text{reactants}}$

• Example: $\text{C} + \text{O}_2 \rightarrow \text{CO}_2$

Energy Transfer and Sign Conventions

• $\Delta E_{\text{system}} > 0$: System gains thermal energy

• $\Delta E_{\text{system}} < 0$: System loses thermal energy

• $w > 0$: Work done on the system

• $w < 0$: Work done on the surroundings

• $q > 0$: Energy flows into the system

• $q < 0$: Energy flows out of the system

• Relationship: $\Delta E = q + w$

Quantifying Heat

Temperature and Heat Transfer

Temperature measures the thermal energy within a sample. Heat is the transfer of thermal energy, always flowing from higher to lower temperature until thermal equilibrium is reached.

• Thermal equilibrium: When two objects reach the same temperature, no net heat transfer occurs.

• Heat transfer equation: $q = C \Delta T$

Heat Capacity

• Heat capacity (C): Quantity of heat required to change the temperature of a system by 1°C. Extensive property (depends on amount).

• Specific heat capacity (C_s): Amount of heat required to raise the temperature of 1 g of a substance by 1°C. Intensive property (does not depend on amount).

• Molar heat capacity: Heat required to raise 1 mole of a substance by 1°C.

Example Calculation

Example: How much heat is absorbed by a penny as it warms from -8.0°C to 37.0°C? Mass = 3.10 g, $C_s$ (Cu) = 0.385 J/g°C.

Thermal Energy Transfer

Heat Exchange Between Substances

When two substances at different temperatures are mixed, heat is transferred from the hotter to the cooler substance until equilibrium is reached.

• Heat lost = - heat gained

Example Calculation

Example: 32.5 g of Al at 45.8°C is submerged in 105.3 g of water at 15.4°C. What is the final temperature at equilibrium? $C_s$ (Al) = 0.903 J/g°C, $C_s$ (water) = 4.18 J/g°C.

Additional info: These calculations use the principle of conservation of energy, setting the heat lost by one substance equal to the heat gained by the other.