An archeologist finds a 1.62 kg goblet that she believes to be made of pure gold. When 1350 cal (5650 J) of heat is added to the goblet, its temperature increases by 7.8 ℃. Calculate the specific heat of the goblet. Is it made of gold? Explain.

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Welcome back, everyone. A group of people doing an exploration came upon an abandoned basement where they found a ring that they think is made of pure titanium. When 15 Jews or 3.59 calories of heat was applied to the ring weighing nine g. Its temperature rose by 3.19 degrees Celsius, determine the specific heat of the ring. And are the explorers correct in their assumption that the ring is made of pure titanium? Note that the specific heat of pure titanium is 0.5 23 jewels per grand times degrees Celsius. We're going to begin by recalling our specific heat capacity formula which relates the heat of a substance represented by the variable Q which is set equal to the mass of that substance. M multiplied by its specific key capacity C which is multiplied by the temperature change. Delta T. Let's recall that the unit for heat Q is going to be in jos. So given the information and the prompt we need to solve for the variable C which is the specific key capacity of the ring. Meaning we would divide both sides of this equation by the product of mass and temperature change. So that those terms will cancel out on the right and that will isolate the specific heat capacity of our titanium or rather the assumed titanium ring. So we'll say the specific heat capacity of the ring where C is equal to the heat of the ring divided by its mass multiplied by the temperature difference or temperature change. And so plugging in our nodes, we would have the heat that is applied to the ring given in the prompt as 15 jewels or 3.59 calories because we want our variable QE or sorry, not our variable Q but our variable C to be in units of jewels per grams, times degrees Celsius. We're going to plug in our term for Q heat in Jews. So we would plug in 15 Jews as given in the prompt. We are then going to divide by the mass of our ring which we are told from the prompt is nine g. And then we would multiply by the temperature difference or temperature change, which is given as 3.19 degrees Celsius. So simplifying we would find in our next line, a specific key capacity of the ring equal to 0.522 jules per gram times degrees Celsius. And based on this value for the specific key capacity of the titanium ring, we would say that that is very close to the specific key capacity of pure titanium, which is equal to from the prompt 0.5 23 jewels per gram times degrees Celsius. So then our final answer is going to be that yes, the explorers are correct about the ring being made of titanium. And so our two final answers are going to be the specifically capacity of the ring, which we calculated as 20.5 22 jules per gram times degrees Celsius. And then the second answer is that yes, the explorers are correct. This completes this example. I hope this made sense and let us know if you have any questions.

An archeologist finds a 1.62 kg goblet that she believes to be made of pure gold. When 1350 cal (5650 J) of heat is added to the goblet, its temperature increases by 7.8 ℃. Calculate the specific heat of the goblet. Is it made of gold? Explain.

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Key Concepts

Specific Heat Capacity

Heat Transfer

Material Identification