You have 750 g of water at 10.0°C in a large insulated beaker. How much boiling water at 100.0°C must you add to this beaker so that the final temperature of the mixture will be 75°C?

Video transcript

Welcome back everybody. We are preparing a insulated pail of water. So let me go ahead and draw our insulated pale and we're preparing it for for dishwashing. Right? So we have our water right here. Now we are told that the initial mass of the water is 4.5 kg and it's at a temperature of 8°C. Now we wish to pour in boiling water to raise the temperature to 61 degrees Celsius. Now, boiling water is going to have a temperature of 100 degrees Celsius and we are asked to find how much water of the boiling water. Do we need to reach this final heat? Now keep in mind specific heat for water is going to be 4180 jewels per kilogram Celsius. Okay, so we know that according to the conservation of heat that the heat lost. Plus the heat gained must be equal to zero. This means that the heat gained is equal to the negative of the heat that is lost. So let's go ahead and plug in some values here. We know that the room temperature water is going to be gaining. Um well, I don't know if it's room temperature, but the colder water is going to be gaining heat. Right? So that's gonna be on the left side of our equation here. So we're gonna have the mass of this water is the specific heat of water, times the change in temperature from the room temperature, water to the final temperature going to be equal to negative. Well, our boiling water is going to be losing heat as it's going down to 61°C. So we'll have the same thing on this side mass of the boiling water. Um times the specific heat of water, times the change in temperature of the boiling water. Right? So let's go ahead and plug in some terms on for for this equation. Right here the mass is 4.5. I'm just gonna leave the specific heat A. C. And you'll see why. Then we have the change in temperature of the water while the final temperature of the cold water is going to be 61 the initial was eight. This is going to be equal to negative the mass of our boiling water, which we don't know. That's what we're trying to find. Times specific heat of water, times the change in temperature of the boiling water, while the final temperature of 61 and the initial temperature was 100. Now I'm going to divide both sides by negative C times 61 minus 100 negative seed, I'm 61 -100 isolating the mass of our boiling water, giving us that the mass of our boiling water is equal to 4. times 53 divided by 39. Giving us that the mass of our boiling water needed is going to be 6.12 kg corresponding to our final answer. Choice of B. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.