512 g of an unknown metal at a temperature of 15°C is dropped into a 100 g aluminum container holding 325 g of water at 98°C. A short time later, the container of water and metal stabilizes at a new temperature of 78°C. Identify the metal.

Video transcript

Hey, everyone. So this problem is dealing with conservation of energy, specifically heat energy. Let's see what it's asking us. An adventurer collects 600 g of an enigmatic MT metal with an initial temperature of eight degrees Celsius. The adventurer immerses this metal in a g copper vessel filled with 420 g of water at 95 degrees Celsius. After a while the temperature of the water, the metal and the copper vessel all reaches an equilibrium at 75 degrees Celsius. Then we're asked to identify the metal in the sample. And so our conservation of energy tells us that the heat energy from the unknown metal plus the heat energy from the copper vessel plus the heat energy from the water all equal zero when they're so. And Q that heat energy is given by the equation MC delta T where the only term that is material dependent is the specific heat capacity or sea. So we're going to solve for this sea of the unknown metal and then it will tell us what met it. So we'll expand all of these terms and isolate the um metal heat terms on the left hand side of the equation subtracting the copper and water terms to the right hand side. So that looks like the mass of the metal multiplied by the specific heat capacity of the metal multiplied by our delta T, which is our T final, which is going to be the same for all three materials because they come to an equilibrium minus our initial temperature of the metal is equal to negative the mass of the copper multiplied by the specific capacity of the copper multiplied by T F minus T initial for the copper. And then all of that minus the mass of the water, specific heat capacity of the water and then T F minus our initial water temperature. And so plugging in for all of the values we know solving for for kind of pulling out that um specific he capacity of the metal, we have the mass of the metal. The problem says 600 g, we're just going to rewrite that as 6000.6 kg to keep everything in standard units, final temperature of 75 degrees Celsius minus an initial temperature of the metal of eight degrees Celsius is equal to an init initial mass or sorry, not initial mass, just mass of the copper of 0. kg multiplied by the specific heat capacity of copper, which we can recall is joules per kilogram seed multiplied by RT final 75 Celsius minus our initial temperature of copper, which is 95 degrees Celsius. And then all of that minus our water terms, initial mass of water is 0.42 kg multiply by a specific heat capacity of water. We can recall is 4186 Jews per kilogram Celsius and then multiplied by again, 75 C minus 95 C. And so when we solve that for our specific heat capacity of this unknown metal, we get Jews per kilogram seed. And then if we look at specific heat capacities of various metals, we can see that, that aligns with aluminum. And so that is the correct answer for this problem that aligns me to answer choice. A that's all we have for this one. We'll see you in the next video.