Thermal Equilibrium (Simplified): Study with Video Lessons, Practice Problems & Examples

Thermal equilibrium occurs when two substances at the same temperature no longer exchange thermal energy. Heat transfers from a hotter object to a colder one, resulting in the hotter object losing heat (negative q) and the colder object gaining heat (positive q). The heat lost by the hot object equals the heat gained by the water, expressed as $q=mc\Delta T$. Understanding this principle is crucial for grasping concepts in thermodynamics and energy transfer.

Thermal Equilibrium (Simplified) Concept 1

Thermal equilibrium is when two substances in physical contact with one another are at the same temperature. Now we're going to say that at the same temperature, these two substances will no longer exchange thermal energy. Now, if we take a look here, we're going to say we're going to initially start out with an object that's at a temperature of 110 degrees Celsius, and I'm going to place it into water at 40 degrees Celsius. So when I do this, there's going to be a heat transfer involved. Always remember that heat moves from a hotter object to a colder object. So by placing the hot cube within the water, we're going to expect the cube to cool off. It's cooling off because it's giving its excess heat to the water. So remember, an object that loses heat has a negative sign for q, and an object that gains heat has a positive sign for q. Water here is gaining the heat of the cube, so it's going to have a positive q. Now, eventually, thermal equilibrium will be reached. At this point, both of them will have the same final temperature. And because of that, we can say that the heat lost by the object is equal to the heat gained by the water. And remember, if your q's or heats are equal to one another, q equals mcat, that means that their mcat values are also equal to each other. So cube object negative cube object equals positive q water, and by extension, negative mcat of the object equals the positive mcat of the water. Now just realize here that under ideal thermal equilibrium, heat transfers only occur between the solvent and the immersed heated object. We don't have to worry about heat being lost between these two. Heat is always moving from the hotter object to the colder object. The hotter object is going to have a negative sign for q since it's going to lose its heat. The colder object initially will gain heat, so it's going to have a positive sign for q. So keep this in mind when giving signs for the q of the object versus the q of water or another object.

If 53.2 g Al at 120.0 ºC is placed in 110.0 g H2O at 90 ºC within an insulated container that absorbs a negligible amount of heat, what is the final temperature of the aluminum? The specific heat capacities of water and aluminum are 4.184 J/g ∙ ºC and 0.897 J/g ∙ ºC, respectively.

• A. 75.579 °C
• B. 92.775 °C
• C. 72.975 °C
• D. 57.972 °C

Here’s what students ask on this topic:

What is thermal equilibrium and how is it achieved?

Thermal equilibrium occurs when two substances in physical contact reach the same temperature and no longer exchange thermal energy. This state is achieved when the heat lost by the hotter object equals the heat gained by the colder object. Mathematically, this can be expressed as:

$q=\mathrm{mc}\Delta T$

where $q$ is the heat transferred, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature. In thermal equilibrium, the heat lost by the hot object (negative $q$) equals the heat gained by the cold object (positive $q$).

How does heat transfer occur between two objects?

Heat transfer between two objects occurs through three primary mechanisms: conduction, convection, and radiation. In the context of thermal equilibrium, conduction is the most relevant. Conduction involves the transfer of thermal energy through direct contact. Heat moves from the hotter object to the colder one until both reach the same temperature. The rate of heat transfer depends on the temperature difference, the thermal conductivity of the materials, and the contact area. The process continues until thermal equilibrium is achieved, meaning no net heat flow occurs between the objects.

What is the significance of the equation q=mcΔT in thermal equilibrium?

The equation $q=\mathrm{mc}\Delta T$ is crucial in understanding thermal equilibrium. It quantifies the amount of heat transferred during a temperature change. Here, $q$ represents the heat transfer, $m$ is the mass of the substance, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature. In thermal equilibrium, the heat lost by the hotter object (negative $q$) equals the heat gained by the colder object (positive $q$), ensuring energy conservation.

Why does heat always move from a hotter object to a colder one?

Heat always moves from a hotter object to a colder one due to the second law of thermodynamics, which states that heat transfer occurs spontaneously in the direction that increases the overall entropy of the system. In simpler terms, thermal energy naturally flows from regions of higher temperature to regions of lower temperature to reach thermal equilibrium. This process continues until both objects reach the same temperature, at which point no net heat transfer occurs, and thermal equilibrium is achieved.

What happens to the temperature of two objects when they reach thermal equilibrium?

When two objects reach thermal equilibrium, their temperatures become equal. At this point, no net heat transfer occurs between them because they are at the same temperature. The hotter object loses heat (negative $q$), while the colder object gains heat (positive $q$), until both temperatures stabilize. This final temperature is somewhere between the initial temperatures of the two objects, depending on their masses and specific heat capacities.