Thermal Equilibrium and Heat Transfer

Thermal Equilibrium

Definition and Key Concepts

Thermal equilibrium occurs when two substances in physical contact with each other reach the same temperature and no longer exchange thermal energy. This is a fundamental concept in thermodynamics and chemistry, as it explains how heat transfer leads to temperature uniformity in a system.

• Thermal Equilibrium: When substances are in contact and at the same temperature, there is no net flow of thermal energy between them.

• Heat Transfer: Heat always flows from the hotter object to the cooler object until equilibrium is reached.

• Direction of Heat Flow: The substance with the higher temperature loses energy, while the substance with the lower temperature gains energy.

Example: If a hot block of metal at 250°C is submerged in a solution at 60°C, the final temperature of the solution will be greater than 60°C but less than 250°C, as heat flows from the metal to the solution until equilibrium is reached.

Illustration of Thermal Equilibrium

• When a hot object is placed in contact with a cold object, heat moves from the hot object to the cold object.

• Once both objects reach the same temperature, they are in thermal equilibrium and heat transfer stops.

Heat Transfer Calculations

To calculate the final temperature when two substances are mixed, the principle of conservation of energy is used. The heat lost by the hot substance equals the heat gained by the cold substance:

$q_{lost} + q_{gained} = 0$

Where:

• $q = m \cdot c \cdot \Delta T$

• m = mass (g or kg)

• c = specific heat capacity (J/g°C or J/kg°C)

• \Delta T = change in temperature (°C)

Practice Problem Example

Problem: 9.2 g of Al at 120°C is placed in 110.0 g H2O at 30°C in an insulated container. The specific heat capacities are:

• Water: $c_{H_2O} = 4.18 \text{ J/g}^\circ\text{C}$

• Aluminum: $c_{Al} = 0.897 \text{ J/g}^\circ\text{C}$

Solution: Set up the equation:

$m_{Al} c_{Al} (T_f - T_{Al,initial}) + m_{H_2O} c_{H_2O} (T_f - T_{H_2O,initial}) = 0$

Solving for $T_f$ gives the final equilibrium temperature. (The answer provided is 30.7°C.)

Summary Table: Key Points of Thermal Equilibrium

Term	Definition	Example
Thermal Equilibrium	State where two objects in contact have the same temperature and no net heat flow occurs	Hot metal in cool water reaches a common temperature
Heat Transfer	Movement of thermal energy from a hotter object to a cooler one	Ice melting in warm water
Specific Heat Capacity	Amount of heat required to raise the temperature of 1 g of a substance by 1°C	Water: 4.18 J/g°C; Aluminum: 0.897 J/g°C

Additional info: Thermal equilibrium is a key concept in both chemistry and physics, underlying calorimetry experiments and energy conservation in chemical reactions.