Heat and Temperature practice questions SOLUTIONS
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1 Heat and Temperature practice questions SOLUTIONS 1. Poor Pluto. One day you're the ninth planet. The next day your the first dwarf planet. To help Pluto with obvious problems of self esteem, we have invented a temperature scale in Pluto's honor. The average temperature on the surface of Pluto is about 34 degrees Kelvin or -239 (remember that absolute zero is 0 degrees Kelvin and -273 ). In the new Pluto temperature scale, zero degrees Kelvin is also zero degrees P, and 34 degrees Kelvin is 1 degree P. a. Liquid nitrogen boils at about What is that in degrees Pluto? (You may round off to the nearest degree Pluto.) If you prefer to work from graphs, then you could draw a graph with degrees Pluto and Celsius on the two axes and pretty much read off the results (especially since you get to round off to the nearest degree P). If you prefer to work with equations, then you need to pick two points, use those two points to come up with the equation for a line, and use that equation to solve the problem. Let s try that. So b. Dry ice keeps things at a chilly temperature of -92. What is that in degrees Pluto? (Round off to the nearest degree P.) If you convert from F to C first, then you can use your equation above to get from C to P. Remember Fahrenheit and Celsius? c. Saturn is always picking on Pluto, pointing out that the atmosphere of Saturn is a balmy 4 degrees Pluto. (This isn't fair since the atmosphere of Saturn is pretty complex, but in places it is a balmy 4 degrees Pluto.) What is that in degrees Celsius? Degrees Fahrenheit?
2 You could try to come up with new equations at this point but it isn't entirely necessary. One way to get a new equation is... d. Water freezes at what temperature Pluto? e. Water boils at what temperature Pluto? grams of water at a temperature of 75 are placed in contact with 30.0 grams of water at a temperature of 25. The system is well insulated so heat cannot escape to the surrounding air, containers, or college students. a. When 100 calories have been lost by the hot water... i. How much heat is absorbed by the cool water? 100 calories (since we assume there is no place else for the heat to go) ii. How many calories are lost by each gram of the hot water? iii. What is the temperature change of the hot water? (lower) iv. What is the temperature of the hot water after 100 calories have been transferred? v. What is the temperature of the cool water after 100 calories have been transferred? Each gram of cool water gains Which makes the temperature b. Okay so let's say a total of 300 calories have been transferred from the 75 water to the 25 water. i. Now what's the temperature of the warmer water? The temperature dropped by three times as much, so the
3 ii. Now what's the temperature of the cooler water? The temperature increase is three times as great, so the c. Not happy yet? Let's say a total of 600 calories have been transferred from the 75 water to the 25 water. i. Now what's the temperature of the warmer water? The temperature drops by six times as much as it did in part a, so the ii. Now what's the temperature of the cooler water? The temperature increase is six times as great as in part a, so the d. If we mix the two samples together, what will be the final temperature? According to part c, equilibrium is reached when the 3. A 100 gram sample of the rock known as basalt is heated to a temperature of 85 and immersed in 100 grams of water which has a temperature of 25. The two are swirled together until an equilibrium reached. Again, he system is well insulated so heat cannot escape to the surrounding air, containers, or college students. a. Keith predicts that the final temperature of the system will be 55 since the water has the same mass as the rock and that exactly halfway between the temperature of the water and the rock. Based on what you have seen in class, do you agree or disagree? What would you predict about the final temperature? Why? Keith is clearly an ignorant dweeb. No rock has a specific heat as high as water (the only things that are close are large organic molecules such as wax and fat). Since the rock will have a lower specific heat, the rock will change temperature more and the final temperature will be closer to the original temperature of the water. So maybe 35 to 45 would be a better guess. b. Well, Keith wasn't even close. The final temperature turned out to be only 35 (how was your prediction?). So as the water increased in temperature from 25 to 35, how much heat was absorbed by the water? 100 grams of water increased in temperature from 25 to 35, so the temperature change was 10. The heat absorbed by the water was c. Your answer to part b actually depends on your knowledge of the specific heat of water. What is the specific heat of water? (Units are important.) d. As the basalt cooled from 85 to 35, how much heat was released by the basalt? (Think carefully, but you shouldn't have to do any calculating.)
4 Same as what was absorbed by the water, since that's where the heat went calories. e. How much heat was released by each gram of the basalt? f. What was the temperature change of the basalt? g. Based on this experiment, what is the specific heat of basalt? Our answer from part e tells us that if the basalt had been "made out of water" it would have only changed temperature by ten degrees. It changed temperature by five times that much. So it must have a specific heat which is five times smaller than that of water (it's "heat equivalent mass" is five times less). In equations, that's (one fifth the specific heat of water) 4. Why is ice cold? Most people would think this is a silly question, but you should know enough about heat and temperature to realize that the answer is actually a little complicated and involved some important principles of thermodynamics. If you take some ice out of the freezer, put it where the something like 20 degrees Celsius above freezing, the ice stays cold and it makes the air around it cold. Why? What's going on here? It is odd, you know. If you cool a piece of iron in a freezer and then bring it out into a room, it will warm up to room temperature. Ice won't do that. What is really odd is that very few non-scientists every think to ask why not. What is happening here is that the ice (which is cold) absorbs heat from the surroundings (which are warmer. Once the ice warms up to zero degrees Celsius it begins to melt. In order to melt it must absorb more heat from the surroundings. It must absorb 80 calories per gram of ice melted, which is a lot. The surroundings cool as a result. This continues only until the surroundings cool to zero degrees C. At that point the ice and the surroundings have the same temperature so heat transfer stops and no more ice melts until the surroundings warm up again. When the surroundings warm up, more heat is transferred, more ice melts, more heat is absorbed from the surroundings, the surroundings cool, and equilibrium is reached when the ice and the surroundings have the same temperature yet again. This is why the melting of ice can be such a slow process, and why the temperature of the ice stays essentially constant at zero degrees C. 5. The heat of vaporization of water is 540 calories per gram and you should know the specific heat of water by now. Imagine that we take 15.0 grams of liquid water at a temperature of 80, put it in a well insulated container, and slowly add 3000 calories of heat.
5 a. What happens as the first 300 calories go into the water? What will we have after those 300 calories have been absorbed? Those first 300 calories get distributed among the 15.0 grams of water. Each gram absorbs 20 calories. So the temperature of the water increases by, making the temperature of the water an even 100. b. As the next 100 or so calories go into the water, does the temperature continue to rise? Why or why not? No, the temperature remains constant at 100 as the water is now boiling. Heat can cause temperatures to change or it can do the other things that energy does. Scientists call these things "work." One form of work is making automobiles go. Another form of work is making the nerves in your brain fire so that you can read this. Another form of work is turning liquids into gases. That's what is happening here. It's called "boiling" or "vaporization." c. You've established what happens as the first 300 calories are absorbed. What happens as the next 2700 calories are absorbed? What does this heat do to the water? It causes the water to boil or vaporize. The liquid water turns to water vapor, which is invisible. If you said that it turns the water into steam you were right but steam is a mixture of water vapor (which is invisible) and water droplets (which aren't). It is hard to predict exactly how many of those droplets will be produced but we know how much water vapor gets produced. That is one gram of vapor for every 540 calories of heat absorbed. d. The heat of vaporization of water is 540 calories per gram. How much liquid water will we have after the last bit of that 2700 calories have been absorbed? (In other words, what will we have after all 3000 calories have been absorbed by the 15 grams of water?) The heat of vaporization of water is 540 calories per gram. So for every 540 calories of heat that gets absorbed by water at 100, a gram of water turns to water vapor. Here we have 2700 calories which is 5 times 540 calories. So that's enough heat to vaporize five grams of water. We started out with 15 grams of liquid water. When we were all done and the system reached its new equilibrium we would have 10 grams of liquid water and 5 grams of water vapor, all at a temperature of 100. By the way, all of thermodynamics is also "just a theory." Thermodynamics has been around for about 150 years and at least for objects of the size that we can see, we've never found a problem with it. Still, it is rightfully called the theory of thermodynamics.
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