Which, if any, of the heat engines in FIGURE EX21.22 violate (a) the first law of thermodynamics or (b) the second law of thermodynamics? Explain.

Video transcript

Hello, fellow physicists today, we're to solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use in order to solve this problem, evaluate the heat engine shown in the figure and determine whether it follows I, the first law or I I the second law of thermodynamics. So our end goal is to solve for two different scenarios or situations. So the first situation that we're trying to solve for are the condition that we're trying to solve for is determine whether our figure follows I the first law. And then our second thing or the second condition that we're trying to solve for is if our figure follows the second law of thermodynamics. OK. So we're given some multiple choice answers. Let's read them off to see what our final answer pair might be. A is I obeys first law I, I obey second law B is I obeys first law I, I violate second law C I violates first law I, I obey second law D is I violates first law I, I violate second law. OK. So first off, let us recall that the engine will follow the first law of thermodynamics. If it satisfies the equation, the heat energy of the hot reservoir is equal to the work out plus the heat and heat energy of the cold reservoir. OK. And let's note that from our figure. So let's take a minute to pause and look at our figure really fast before we go any further. So in red, in this little red RR rectangle, we have the hot reservoir and its temperature is Kelvin. And in this blue rectangle, we have the cold reservoir which is Kelvin. So the heat energy released from the hot reservoir is 600 Jews and then the heat energy from the cold reservoir is 300 Jews. And then the workout as shown in the figure here is 250 jewels. So let's write that all that information down really quick. So we don't forget. So Qh is equal to Jews QC. So the heat energy, the hot reservoir, 600 Jews, the heat energy, the cold reservoir is 300 tools and the workout is jewels. OK. Awesome. Awesome. So now we need to take our work out value and add it to the heat energy of the cold reservoir to see if it will equal 600 Jews. If it equals 600 Jews, then it will be satisfied. So the first law thermodynamics will be obeyed. And if it doesn't add up to 600 it will be violated. So let's see. So jewels plus jewels is equal to Jews. So it does not equal 600. So that means that the first law of thermodynamics is violated. So that is our first answer. For part I, so now to solve for part I I, we need to recall and use the equation for the carno efficiency of an engine. So the equation for the carno efficiency of an A of an engine is represented by a AC is equal to one minus the temperature of the cold reservoir divided by the temperature of the hot reservoir. So let's plug in all of our known variables to solve for the Carno efficiency of an engine. So the temperature of the cold reservoir was Kelvin divided by the temperature of the hot reservoir which was 900 Kelvin. So when we plug that into a calculator, the carno efficiency of an engine will be equal to 0.61. Now we need to recall and use the equation for the efficiency of an engine which in this case, the efficiency of an engine is represented or denoted with just A and A is equal to the work out divided by the heat energy of the hot reservoir. So now we can plug in our known variables to solve for the efficiency of an engine which is equal to 250 jewels divided by Jews, which is equal to let me plug into a calculator, 0.42. So in this case, the efficiency of an engine is less than the carno efficiency of an engine. Therefore, the engine obeys the second law of thermodynamics. And we did it everyone we saw for both parts. I and I, I, so let's look at our multiple choice answers to see what the correct answer is. And it appears that the letter C is our correct answer. I violates the first law. I, I obeys the second law. Thank you so much for watching. Hopefully that helped and I can't wait to see in the next video. Bye.