thermal equilibrium is when two substances in physical contact one another or at the same temperature. Now we're going to say at the same temperature, these two substances would no longer exchange thermal energy. Now, if we take a look here, we're gonna say, we're gonna initially start out with a object that's at a temperature of 110°C, and I'm gonna place it into water at 40°C. 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 gonna expect to 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 cube water here is gaining the heat of the cube, so it's going to have a positive cube. Now, eventually the 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 cues or heats are equal to one another hue equals. And cat, that means that they're m cat values are also equal to each other, So cuba object, negative view object equals positive Q. Water and by extension, negative M cat of the object equals the positive M cat 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 cues, and it's gonna 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 queue of the object versus the queue of water or another object.