Constant-Pressure Calorimetry Example 2

Jules Bruno
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here, we're told when 60 g of lead at 68.3 degrees Celsius is poured into 90 g water at 30 degrees Celsius. Within a coffee cup calorie meter, the temperature increases to 48 degrees Celsius. Based on this information, what is the heat capacity of the calorie meter? We're told the specifically capacity specific heat of lead in water are 0.1 to 8 and 4.184 respectively. All right, so we're gonna plug. Well, first of all, we need to realize we have our container with water and we're placing it placing into it. Our lead lead is at a higher temperature than the water is. Remember, the hotter object always releases its heat, so it's gonna release its heat. So the water is releasing its heat. So negative Q of water? No negative. You bled? Sorry. The object that's releasing its hey, he equals positive Q of water, which is absorbing it, plus Q of the calorie meter. The calorie meter is absorbing some of it as well because they tell us that we need to find a T capacity. We don't need to find a T capacity. If it was involved with in the calculation. All right, so if their cues are involved, that means they're m. Katz for some of them are involved. So negative m cat of our lead equals positive and cat of the water Remember calorie emitters. Their masses tend to be unknown, so it's just the heat capacity that they have times the change in temperature. Alright, so here we're gonna say negative 60 g of our lead times. It's specific heat capacity, times the change in temperature. We're told that the temperature increases to 48 degrees Celsius that the final temperature for everyone. So here the change in temperature for the lead is the final temperature, minus its initial temperature of 68.3 degrees Celsius. That equals positive and cat of water and cat um so water is 90 g of water times. It's specific heat capacity times its final temperature minus the initial temperature that it had. Plus, we don't know the heat capacity of the Cal. Where matter? That's what we're looking for. And here's the thing. Before we add the lead to the water. It was just the water in the calorie Mitter hanging out with each other so they both must have been at the same initial temperature, so change in temperature would be 48 degrees Celsius minus the initial temperature of the calorie meter, which again it was with water and we assume they both were at the same initial temperature of 30 degrees Celsius. All we have to do now solve for this one missing variable. So what we're gonna do now is we're going to multiply everything here on this side. Grams will cancel out. Degrees Celsius will cancel out, will have jewels left on this side, which comes out to 1. 55.904 jewels equals grams. Cancel out degrees Celsius, cancel out. So we're gonna have everything here also in jewels. So that is 6778.8 jewels. Plus, when you subtract these, that's gonna give me 18 degrees Celsius times my specific capacity or my heat capacity of C gotta We gotta isolate our heat capacity of C. So next we're going to subtract this from both sides here. So when we do that, we're gonna have now negative 66. actually, negative. 66 to 2 point 176 equals 18 degrees Celsius. Times my heat capacity of seat divide out 0 degrees Celsius. Remember Jules air still here? So 18.0 degree Celsius heat capacity is a number that is positive, So this is an absolute terms. When we do that, that's jewels divided by degrees Celsius. So here my heat capacity, which is capital C, equals 3 67. jewels over degrees Celsius. So that would be the heat capacity of our calorie emitter within this given question.