Thermal Equilibrium in GOB Chemistry: Concepts and Applications

Thermal Equilibrium

Definition and Key Concepts

Thermal equilibrium occurs when two substances in physical contact reach the same temperature and no longer exchange thermal energy. This is a fundamental concept in thermodynamics and is essential for understanding heat transfer in chemical and biological systems.

• Thermal energy is transferred from the hotter object to the cooler object until both reach the same temperature.

• At thermal equilibrium, the net heat flow between the substances is zero.

Process of Reaching Thermal Equilibrium

The process can be visualized in three stages:

• Initial States: Two objects at different temperatures (e.g., T1 = 110°C, T2 = 40°C).

• Heat Transfer: Heat moves from the hotter object to the cooler object.

• Final States: Both objects reach the same temperature, and thermal equilibrium is established.

Stage	Description	Diagram
Initial States	Objects at different temperatures	Thot = 110°C, Tcold = 40°C
Heat Transfer	Heat flows from hot to cold object	Qlost (Object) = Qgained (Object)
Final States	Both objects at the same temperature	Tfinal = Thot = Tcold

Ideal Thermal Equilibrium

Under ideal thermal equilibrium, heat transfers only occur between the solvent and the immersed heated object, with no loss to the surroundings.

Example Problem

Example: If a 50 g block of lead at 250°C is submerged in a solution at 90°C, the final temperature of the solution will be:

• a) Equal to 90°C

• b) Greater than 90°C

• c) Less than 90°C

Explanation: The final temperature will be greater than 90°C because the hot lead block will transfer heat to the solution, raising its temperature above the initial 90°C.

Application: Calculating Final Temperature

To determine the final temperature when two substances are mixed, use the principle of conservation of energy:

• Heat lost by the hot object = Heat gained by the cold object

The formula for heat transfer is:

$q = m c \, \Delta T$

• q: heat energy (J)

• m: mass (g)

• c: specific heat capacity (J/g·°C)

• ΔT: change in temperature (°C)

For two substances:

$m_1 c_1 (T_{final} - T_1) = -m_2 c_2 (T_{final} - T_2)$

Where:

• Tfinal: final equilibrium temperature

• T1: initial temperature of substance 1

• T2: initial temperature of substance 2

Practice Problem

If 53.2 g of Al at 120.0°C is placed in 110.0 g H2O at 90°C within an insulated container, what is the final temperature? Use the following specific heat capacities:

• Aluminum: 0.897 J/g·°C

• Water: 4.184 J/g·°C

Set up the equation:

$m_{Al} c_{Al} (T_{final} - T_{Al}) + m_{H_2O} c_{H_2O} (T_{final} - T_{H_2O}) = 0$

Solve for Tfinal to find the equilibrium temperature.

Additional info: The notes focus on the concept of thermal equilibrium, heat transfer, and practical calculation methods, which are central topics in GOB Chemistry.