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define-thermal-equilibrium

🚀 Thermal equilibrium is a fundamental concept in thermodynamics that describes the state of a system when it is in balance with its surroundings in terms of temperature. When two systems are in thermal equilibrium, there is no net heat transfer between them, meaning they are at the same temperature. This concept is crucial for understanding how heat energy flows and how systems interact with each other. The temperature is a measure of the average kinetic energy of the particles in a substance, and when two objects are at the same temperature, their particles have the same average kinetic energy, leading to no heat exchange.

Theory Explanation

Understanding Temperature

Temperature is a measure of the average kinetic energy of the particles in a substance. It is an important parameter in thermodynamics as it determines the direction of heat flow between systems. Heat flows from a hotter object (higher temperature) to a cooler object (lower temperature) until thermal equilibrium is reached.

\[ T = \frac{1}{N} \sum_{i=1}^{N} KE_i \]
Defining Thermal Equilibrium

Thermal equilibrium occurs when two systems in thermal contact do not exchange heat. This means that the temperatures of the systems are equal. If two objects are in thermal contact and are not at the same temperature, heat will flow from the hotter object to the cooler one until they reach the same temperature, achieving thermal equilibrium.

Conditions for Thermal Equilibrium

For thermal equilibrium to occur, the systems must be in thermal contact and isolated from other influences. This means that no external heat sources or sinks should affect the systems. Once thermal equilibrium is achieved, the systems can be considered to be in a stable state with respect to temperature.

Key Points

  • 🎯 Thermal equilibrium means no net heat transfer between systems.
  • 🎯 Temperature is a measure of average kinetic energy of particles.
  • 🎯 Two systems in thermal equilibrium have the same temperature.

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Examples:💡

Example 1: Two metal blocks, one at 100°C and the other at 20°C, are placed in contact. What will be their final temperature when they reach thermal equilibrium?

Solution:

Step 1: Calculate the final temperature using the principle of conservation of energy. Let m1 and m2 be the masses of the blocks, and c1 and c2 their specific heats. The heat lost by the hot block equals the heat gained by the cold block: m1 * c1 * (T_initial1 - T_final) = m2 * c2 * (T_final - T_initial2).

\[ m_1 c_1 (T_{initial1} - T_{final}) = m_2 c_2 (T_{final} - T_{initial2}) \]

Step 2: Assuming equal masses and specific heats for simplicity, we can set m1 = m2 and c1 = c2. Thus, T_final = (T_initial1 + T_initial2) / 2 = (100 + 20) / 2 = 60°C.

\[ T_{final} = \frac{T_{initial1} + T_{initial2}}{2} = \frac{100 + 20}{2} = 60°C \]

Example 2: A glass of water at 25°C is placed in a refrigerator at 5°C. What happens to the temperature of the water?

Solution:

Step 1: The water will lose heat to the refrigerator until it reaches thermal equilibrium with the refrigerator. The final temperature will be 5°C when thermal equilibrium is achieved.

Step 2: Since the refrigerator is at a lower temperature, heat will flow from the water to the refrigerator until both reach 5°C.

Common Mistakes

  • Mistake: Students often confuse thermal equilibrium with thermal isolation. They think that thermal equilibrium means no heat transfer at all, rather than no net heat transfer.

    Correction: Clarify that thermal equilibrium refers to the state where two systems have equal temperatures and thus no net heat flow occurs.

  • Mistake: Some students believe that thermal equilibrium can be achieved instantly, not realizing that it takes time for heat to transfer between objects.

    Correction: Emphasize that thermal equilibrium is a process that occurs over time as heat is exchanged between systems.

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