Thermal Equilibrium - Online Tutor, Practice Problems & Exam Prep

Thermal equilibrium occurs when two substances at different temperatures come into physical contact and reach the same temperature, ceasing the exchange of thermal energy according to the first law of thermodynamics. In this state, the heat lost by the hotter object (negative Q) is equal to the heat gained by the colder one (positive Q), as represented by the equation:

$Q=mc\Delta T$

where m is mass, c is specific heat capacity, and ΔT is the change in temperature. If the system is not ideal, the calorimeter or container may also absorb heat, modifying the equation to include the heat absorbed by the calorimeter (Q of the container). This concept is crucial in understanding energy transfer and the approach to thermal balance in physical systems.

Thermal Equilibrium

Thermal equilibrium is when 2 substances in physical contact of one another are at the same temperature. Now at the same temperature, these two substances would no longer exchange thermal energy by way of the first law of thermodynamics. So if we take a look here, let's say we have this heated metal cube here and it's initially at a temperature of 110�C and we're going to place it into water at 40�C.

Remember, heat transfers when it comes to heat. It always moves from hotter to colder object. So the cube will be losing some heat. So some of the heat from the cube will be lost and it's going to go into the water. So we'd say here that the cube is losing heat, so it would have a negative cube, and the water is absorbing that heat, so it would be a positive cue for the water. Eventually though, the queue will no longer be able to release any more heat because it'll get to the same temperature as the water. O it's at that moment we've reached thermal equilibrium.

Now, at thermal equilibrium, we can say here that they're both going to have the same heat, so the negative Q of the object hotter object would be equal to the positive Q of water in this case. And if their queues or heats are equal to one another, then their M cap formulas are equal to each other because remember Q equals MCAT, so negative MCAT equals positive MCAT. Now under ideal thermal equilibrium, heat transfers only occur between the solvent and the immersed heated object.

If the situation is not ideal then then we can say that that additional HE could be absorbed by the calorimeter. So the calorimeter or the container in this case same thing would absorb some of that heat of the object. O here this equation would expand out under non ideal conditions to be negative Q of the object equals positive Q of the water plus Q of the container also known as the calorimeter. So just remember if your rofessor is mentioning that this is a pure thermal equilibrium type of question, then you could just say Q negative Q hotter object equals positive Q of colder object. But if the calorimeter is involved, you have to take into account that it too would absorb some of this heat that's coming off of the hotter object.

Thermal Equilibrium Example 1

Here in this example question it says if 50g block of lead at 250�C it's submerged in a solution at 90�C the final temperature of the solution will be. So let's just think about it. We have a container. We have a hot piece of lead here being submerged in some colder water. So try to use everyday real experiences here. What happens?

I take a hot pan and I dunk it into the sink filled with water. We'll hear the pan sizzle. That's because the pan is releasing its extra heat into the water. The water is becoming vaporized. Remember, at thermal equilibrium, they're both going to reach a temperature that's the same for both of them.

The temperature that they reach should be a temperature somewhere between 150�C and 90�C, because we'd expect the hotter object to release enough heat so that it and the solvent that it's in can reach the same temperature. So the hotter object cools down some, the colder object warms up some. Their new final temperature will exist somewhere between their two initial temperatures, so we'd expect that the temperature of the solution to be greater than 90�C. It'll be a number between 150 and 90�C.

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?

Thermal equilibrium is a concept in thermodynamics that describes a state where two objects or systems in physical contact with each other exchange heat energy until they reach the same temperature. At this point, there is no net flow of heat between the objects; the amount of heat leaving one object is equal to the amount of heat entering it from the other object. When thermal equilibrium is achieved, the systems are said to be at the same temperature and there is no further change in their thermal properties. This is a fundamental principle underlying the zeroth law of thermodynamics, which states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This principle allows us to use thermometers to measure temperature objectively.

What does it mean when we say that an object is in thermal equilibrium?

When an object is in thermal equilibrium, it means that it has reached a state where there is no net exchange of heat energy with its surroundings. This occurs when the object and its environment are at the same temperature, so heat, which naturally flows from hotter to cooler regions, no longer transfers between them. In this state, all parts of the object and its immediate environment are at a uniform temperature. Thermal equilibrium is a key concept in thermodynamics, and it's essential for understanding how heat transfer works. It's also the principle behind thermometers, which measure their own temperature change until they reach thermal equilibrium with the object or environment they are measuring, thus indicating the temperature.

How do you calculate the temperature of thermal equilibrium?

To calculate the temperature of thermal equilibrium, you need to consider the principle that when two objects of different temperatures are in thermal contact, heat energy will transfer from the hotter object to the cooler one until they reach the same temperature. This final temperature is the temperature of thermal equilibrium.

If you are dealing with two substances, you can use the formula:

$\left(Q_{\text{lost}}\right)+\left(Q_{\text{gained}}\right)=0$

where Q represents the heat energy lost or gained, which can be calculated using the specific heat capacity equation:

$Q=mc\Delta T$

Here, 'm' is the mass, 'c' is the specific heat capacity of the substance, and 'ΔT' is the change in temperature.

For two objects, the equation becomes:

$\left(m_1\right)\left(c_1\right)(T_f-T_1)+\left(m_2\right)\left(c_2\right)(T_f-T_2)=0$

Solve for Tf, which is the final temperature of thermal equilibrium. You'll need to know the initial temperatures (T1 and T2), masses (m1 and m2), and specific heat capacities (c1 and c2) of the two substances involved.