Calculate the energy to heat two cubes (gold and aluminum) each with a volume of 10 cm³ from 15 °C to 25 °C. Refer to Tables 2.8 and 3.11.

Question

Accepted Answer

Welcome back, everyone. We need to determine the energy required to heat the two cylinders, one made of tin and the other composed of tungsten from 25 Celsius to 45 Celsius. If each has a volume of 25.0 cubic centimeters, we're given two diagrams of each of our metals with their corresponding volumes in cubic centimeters. Specific heats in joules per grams times degrees Celsius and their densities given in grams per cubic centimeter. We're going to need to begin by recalling our formula for specific heat capacity, which is defined by the variable C and is found from taking the heat of our substance expressed by Q divided by its mass times delta T. The difference in temperature, we can isolate defined Q or heat by multiplying both sides by mass times the difference in temperature. So that those terms cancel out on the right. And we'll find that the heat of our substance or thermal energy required is found from taking our specifically capacity multiplied by the mass of our substance times delta T. Now, in relation to our prompt, we're going to need to find our total thermal energy required to heat our two metal cylinders by finding Q total and setting that equal to the heat of our tin plus the heat of our tungsten. Now, we need to begin by finding our mass of 10, which we can utilize our density formula where row is related to mass over volume. So finding our mass of 10, we would say that we would take row times volume. In this case, our density of 10 times the volume of Tin. So plugging in our density, we're given a value of 7. g per cubic centimeter as our density of tin, we're going to need to multiply by our given volume of 10. From our prompt being 25.0 cubic centimeters, which will allow us to cancel out our units of cubic centimeters leaving us with grams for mass. And we'll find that our mass of 10 is equal to 181.625 g. Next, calculating our mass of tungsten, we again have the density of tungsten multiplied by the volume of tungsten. So plugging in our density from our diagram, we're given 19.30 g per cubic centimeter multiplied by our volume for the tungsten container. Also being 25.0 cubic centimeters, canceling out cubic centimeters. We'll find from our product, our massive tungsten being 482. g. Next, we're going to need to calculate delta T which is found from taking our final temperature minus the initial temperature. So based on our prompts, we have an initial temperature For both cylinders being 20 sorry, a final temperature for both cylinders being degrees Celsius subtracted from the initial temperature for both cylinders being 25 degrees Celsius. And this will give us a difference in temperature equal to 20 degrees Celsius. So now with delta T, we're going to find our total energy required Q total to heat our two cylinders to 45°C, where we would take our heat of 10 using our specific heat capacity formula. That would be the mass of 10 times its specific heat capacity times the delta T of 10. And this is added to our mass of tungsten times the specific capacity of tungsten times the delta T of tungsten difference in temperature plugging in our knowns to find Q total to get to degrees Celsius. For both cylinders, we have our mass of 10 which we found above as 181.6 25 g multiplied by our specific heat capacity of 10. Given in our diagram as point 2270 Jews per grams times degrees Celsius multiplied by delta T which we determine to be 20 degrees Celsius making some more room for our calculation. This is then added to our mass of tungsten which we determined above to be 482.5 g times our specific heat capacity of tungsten, which we determined or which was given to us in our diagram as 0.1320 Jews divided by grams times degrees Celsius, which is then multiplied by delta T 20.0 degrees Celsius. So now simplifying in our next line, we'll find that we have The sum between 824.578, canceling out our unit of grams as well as Celsius that leaves us with Jews and this is added to 1273.8 Jews. Once we cancel our unit of grams and Celsius. So these are the sums between our specific heat capacities of both of our metals. And we'll find that the total amount of thermal energy needed to increase the heat to 45 Celsius for both of our containers is equal to 2,098 jewels. So our final answer is 2,098 jewels. I hope that this made sense and let us know if you have any questions.

Calculate the energy to heat two cubes (gold and aluminum) each with a volume of 10 cm³ from 15 °C to 25 °C. Refer to Tables 2.8 and 3.11.

Verified video answer for a similar problem:

Key Concepts

Specific Heat Capacity

Density

Energy Calculation

Calculate the energy to heat two cubes (gold and aluminum) each with a volume of 10 cm3 from 15 °C to 25 °C. Refer to Tables 2.8 and 3.11.

Verified video answer for a similar problem:

Key Concepts

Specific Heat Capacity

Density

Energy Calculation

Calculate the energy to heat two cubes (gold and aluminum) each with a volume of 10 cm³ from 15 °C to 25 °C. Refer to Tables 2.8 and 3.11.