A 32.5-g iron rod, initially at 22.7 °C, is submerged into an unk...

Question

A 32.5-g iron rod, initially at 22.7 °C, is submerged into an unknown
mass of water at 63.2 °C, in an insulated container. The
final temperature of the mixture upon reaching thermal equilibrium
is 59.5 °C. What is the mass of the water?

Accepted Answer

Hey everyone, we're told that whiskey rocks are small cubes of natural stone. Used to chill whiskey and other spirits. To test its effectiveness, it was used in an unknown amount of water. We're told that three rocks that collectively weigh 95.5 g that were initially at eight degrees Celsius were placed in an insulated container full of water at 27.1 degrees Celsius. And the specific heat of the rocks is 0.98 jewels per grams times kelvin were asked to calculate the mass of water. Considering that the final temperature is 13.6 degrees Celsius First, let's go ahead and determine the initial temperature of our rocks and our water. So starting off with the initial temperature of our rocks, We want to convert this into Calvin's. So we'll take that 8°C and we're going to add 273.15. This will get us to a value of 281.15 Kelvin. Now, let's go ahead and determine the initial temperature of our water. Again, we're going to take that initial temperature of 27.1°C and add 273.15. This will get us to a total of 300. Kelvin. And lastly to calculate the final temperature, We're going to take 13.6°C and add 273.15 and end up with a final temperature of 286.75 Kalfin. Now let's go ahead and calculate the mass of water. We can do so by using the formula Q equals mass times the specific heat times the change in temperature que being our heat. And since we are in an insulated container, we know that the queue of our rocks is equivalent to the negative Q. Of our water. Again with Q being our heat. Now to plug in our values, we know that the mass of our rocks is 95.5 g And we're going to multiply it by its specific heat which is 0.98 jewels over g times kelvin. Taking our change of temperature, we have a final temperature of 286.75 Kelvin. And we're going to subtract our initial temperature Which was 281.15 Kelvin, this is going to be equivalent to the negative Q. Of our water. So since the missing variable here is going to be the mass of our water, we can go ahead and pull it out And multiply it by the specific heat of water which is 4.184 jewels over g times Calvin. And to multiply the change in temperature which is 286. Kelvin - Our initial temperature of water which is 300.25 Kelvin. Now let's go ahead and simplify this a bit further. So we end up with 93.59 jewels over Kelvin. When we multiply our 95.5 times are 0. And this is going to be multiplied by 5.6 Kelvin. This is going to be equivalent to the negative mass of our water times -56. jules over grams. Simplifying this a bit further, we get 524.104 jewels equals the negative mass of our water times negative 56. jewels over g. To isolate our massive water. We can go ahead and divide both sides by negative 56.484 jewels over g. This will get us to a total of 9.28 g for the mass of our water. And this is going to be our final answer. Now, I hope that made sense. And let us know if you have any questions.

A 32.5-g iron rod, initially at 22.7 °C, is submerged into an unknown mass of water at 63.2 °C, in an insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 59.5 °C. What is the mass of the water?

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