Okay for this problem, It's not too tough. It just requires a little bit of keeping track. Of things were given the following scenario. We have an unknown metal. We call it my junk metal. We have a sample of copper metal and we also have a constant pressure. Keller immature with water in it. And I know the mass for each of these and the mass for my unknown metal is 20.3 grams. The massive my compra mental is 28.5 grams and the mass of my water is exactly 100. Gramps, make that a little bit easier to read. Okay, I also know my initial temperature for each one of these in the initial temperature for each metal is 80.6 degrees c and the initial temper for temperature for the water is 11.2 degrees C. And I also know final temperature for all three. And that's the same for all three 13.7 degrees Celsius, 13.7 degrees Celsius and 13.7 degrees Celsius. Okay, Now I could look up the specific heat for copper, and that is 0.3 85 J over GC degrees and water specific heat is 4.184 j over GC degrees. That should be everything I need. Let's go back and make a plan, and I want to make sure my cameras on and it is. So let's switch colors and make a plan for a plan. Step one. We're gonna find q of the water, and we're going to use Q equals M C Delta T Step two. We're gonna find que for the copper using the same formula and Step three. We know that Q of the water equals que of my unknown plus you of the copper. And if you'll recall, we just calculated this in this so we will be able to figure out queue for the unknown. And then q of the unknown equals the mass of the unknown, which we know see, which is are unknown plus the delta T which we know. So we're going to solve Um, let's we're going to solve this equation for Let me get my We're going to solve this equation for C, and then we'll be done. Let me get my pin back here and we will start on the next page. Okay, Step one Q for water Mass was 100 grams. C is 4.184 j over GC degrees, and my delta T is ah for water. It's gonna end up being. I'm gonna jot this down here 13.7 degrees C, minus 11.2 degrees C, and that equals 2.5 degrees Celsius. So solving for Q for water punching all those numbers in the calculator, we get 1000 46 jewels. There's our first Q. Now let's dio Q four cop perk you Where. Copper Same equation. We just have different numbers. We're gonna have 28.5 grams, gonna have 0.3 85 j over GC degrees, and our delta T will be 80.6 degrees C, minus 13.7 degrees C, and that is 66.9 degrees c. Do the math for my copper and we get 700 34 0.1. Jules. Okay, our third order of business. We know that Q H two is equal to queue of are unknown plus Q of our copper, and we know this value in this value, so cue over unknown is going to equal que over age 20 minus que of the copper And we just found those values. So it'll be 10 for six Jules minus 734.1 jewels, and that will eke well, 311. Let's make it 312 Jules. And that equals Q of the unknown. Okay, Last and final step for the unknown Sea of the unknown equals que over mass and delta t And let's all sub in Seoul. So we said 312 and we're dividing that by 20.3 grams and 66 0.9 degrees C. And I'm gonna double check because I think when I did this the first time, I used to money Sig Figs for my I used 3 11.9 So let me punch these. Make sure rounds the same. Yes, it does. So when I round to the correct numbers Sig Figs here I get zero point 230 j over G C. Degrees and there it is. Problem solved.