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Ch 17: Temperature and Heat

Chapter 17, Problem 17

A nail driven into a board increases in temperature. If we assume that 60% of the kinetic energy delivered by a 1.80-kg hammer with a speed of 7.80 m/s is transformed into heat that flows into the nail and does not flow out, what is the temperature increase of an 8.00-g aluminum nail after it is struck ten times?

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Welcome back everybody. We are taking a look at a hammer that is hitting an iron block. We're told that the mass of the hammer is 2.5 kg. Were told that it moves at a velocity of 10.2 m per second. We are told that the mass of this iron block that that is it is hitting is 500 g. Now we are tasked with finding what the transferred heat is. No, my apologies. The gain in temperature is So what this delta T. Is right here after the block is hit eight times. Well, I started as you see, I started writing out the formula we're going to need to use which is Q equals M C, delta T. And delta T. Is exactly what we want. But we don't have Q. We don't have em and we don't have see what we do have mm is going to be the mass of our block right here. But we still need the specific heat and the queue. Well, the heat transferred is just going to be the amount of heat transferred from the hammer to the block for every single hit. Since they're eight hits, this will be eight times the kinetic energy of the hammer. So this will be eight times while the formula for kinetic energy is one half times mass times velocity squared. Now this is going to be the mass of our hammer. So let's go ahead and plug in all of these values. We have that. Our heat is eight times one half times the mass of our hammer, which is 2.5 times our velocity of 10.2 which gives us 1040 jewels. Since we are dealing with an iron block as well, you can actually look up the specific heat and it says that it is 10400.450 joules per gram Celsius. Now that we have our heat, our specific heat and our mass we are go ahead. We are ready to find delta T. First. Let's isolate that delta T. Term. We have the Q. Is equal to M. C. Delta T. In order to get that by itself. I'm gonna divide both sides by M. C. As you can see on the right hand side, the EMC on top and bottom cancel out. And we get that delta T. Is equal to Q. Over M. C. So let's go go ahead and plug in our values here we have 1040 jewels of energy are transferred from the hammer to the block. Times the mass of our block which is 500 g times our specific heat of 0.450. Which when you plug all of this in your calculator, we get that. The temperature gain in the block is 4.62 degrees Celsius corresponding to answer choice. A thank you all so much for watching. Hope this video helped. We will see you all in the next one
Related Practice
Textbook Question
Two rods, one made of brass and the other made of copper, are joined end to end. The length of the brass section is 0.300 m and the length of the copper section is 0.800 m. Each segment has cross-sectional area 0.00500 m^2 . The free end of the brass segment is in boiling water and the free end of the copper segment is in an ice–water mixture, in both cases under normal atmospheric pressure. The sides of the rods are insulated so there is no heat loss to the surroundings. (b) What mass of ice is melted in 5.00 min by the heat conducted by the composite rod?
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Textbook Question
In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200-W electric immersion heater in 0.320 kg of water. (b) How much time is required? Assume that all of the heater's power goes into heating the water
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Textbook Question
While painting the top of an antenna 225 m in height, a worker accidentally lets a 1.00-L water bottle fall from his lunchbox. The bottle lands in some bushes at ground level and does not break. If a quantity of heat equal to the magnitude of the change in mechanical energy of the water goes into the water, what is its increase in temperature?
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Textbook Question
(a) Calculate the one temperature at which Fahrenheit and Celsius thermometers agree with each other.
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Textbook Question
(b) Calculate the one temperature at which Fahrenheit and Kelvin thermometers agree with each other
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Like the Kelvin scale, the Rankine scale is an absolute temperature scale: Absolute zero is zero degrees Rankine (0°R). However, the units of this scale are the same size as those of the Fahrenheit scale rather than the Celsius scale. What is the numerical value of the triple-point temperature of water on the Rankine scale?
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