How much work is done by the environment in the process shown in FIGURE EX10.39? Is energy transferred from the environment to the system or from the system to the environment?

Video transcript

Hey everyone, let's go through this practice problem. The figure below shows the process in which work is done by the environment common. Whether energy transfer occurs from system to environment or vice versa. Option, a environment system, option B system to environment, option C, no energy transfer or option D cannot be determined. So for this problem, the main clue we're given is a figure that shows the amount of energy and the way it's allocated in a system in two different states, we're given the initial kinetic energy and the initial potential energy and we're given the final kinetic energy, the final potential energy and the change in thermal energy of the system. The figure also mentions that there is some quantity of external work done either on or by the system. But the figure doesn't tell us how much of that is the quantity of that external work is actually going to be the key to this problem. If that amount of external work is a positive number, then that means energy is being transferred from the system or from the environment to the system. But if that external work is a negative number, then that means the system is losing energy to the environment. So the main thing we want to do in this problem is find the quantity of that external work. And we can do that using the law of conservation of energy, which states that since energy can't be created or destroyed, then the initial energy variables, the sum of the initial energies could be equal to the sum of the final energies. So in other words, K sub I plus the U sub I plus the external work is equal to the final kinetic energy plus the final potential energy plus the change in thermal energy. Unfortunately, for us, most of these variables are simply given to us in the problem. So the initial kinetic energy is given to us in the graph as five Jews, the initial potential energy is given in the graph as two jewels. The external work is something that's unknown to us right now. The final kinetic energy is one jewel. The final potential energy is given as four jewels and the change in thermal energy is given as three Jes. So five plus two is seven. So that's seven jewels plus the external work is equal to one plus four plus three, which is just going to be eight Jews. We can subtract both sides of the equation uh from we can subtract seven Jews from both sides of the equation. Solve for W sub X and that's just one jewel. So the external work done is one jewel and that is a positive number which means that due to this external work, the system is gaining energy. In other words, energy is being transferred from the environment to the system and that is it for this problem. I hope this video helped you out and please consider checking out some of our other videos which will give you more experience with these types of problems, but that's all for now and I hope you all have a lovely day. Bye bye.