As a new mechanical engineer for Engines Inc., you have been assigned to design brass pistons to slide inside steel cylinders. The engines in which these pistons will be used will operate between 20.0°C and 150.0°C. Assume that the coefficients of expansion are constant over this temperature range. (a) If the piston just fits inside the chamber at 20.0°C, will the engines be able to run at higher temperatures? Explain

Video transcript

Welcome back everybody. We are taking a look at this system right here on the left hand side, we have a piston right now. This piston is going to be moving into a barrel. So I'm just gonna draw kind of the casing of of the barrel here. Right now inside this barrel, you have some some fluids and this entire system is meant to work in a temperature range right of Anywhere from 10°C all the way up to 180°C. Now, the piston is made of aluminum and the barrel is made of oper and we are asked If, well actually, before we address the question here, we are also told that at 10°C, the entire system does work. Now, Then we are asked as the temperature increases past 10°C, will the system continue to work well? We know that as temperature increases. So will the the sizes of each of our components. Now, let's think about this theoretically here. If the size of the piston becomes greater than the barrel, the system will not work as the piston will have a tough time sliding into the barrel or not even fit at all. Now, if the barrel is bigger than the piston, the system will work, it may not be the tightest of fits, but the piston will still slide inside the barrel. So, what we are really comparing is the expansive it ease of each metal here, which I have them listed right here. We have that the expansive itty of aluminum Is equal to 2.4 times 10 to the -5C to the -1. And then we have let's see here that the expansive itty of copper Is equal to 1.7 times 10 to the -5. As you can see, the expansive itty of aluminum is greater than that of copper, meaning that as the temperature increases, the size of the piston will become bigger than the barrel, which by our earlier conversation, means that the system will not work as the piston increases and expands much more than the copper corresponding to our answer. Choice of D. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.