 An inventor claims to have developed a heat engine which receives 700 kJ of heat from a source at 500 Kelvin and produces 300 kJ of network while rejecting the waste heat to a sink at 290 Kelvin. Is this a reasonable claim? Why or why not? Well, we have a heat engine, and we know that the high-side temperature is 500 Kelvin and that the low-side temperature is 290 Kelvin. It receives 700 kJ of heat transfer in and produces 300 kJ of network. Because these are magnitudes, I will get rid of the dots. And the way that we can evaluate if it's a reasonable claim or not is to compare the thermal efficiency to the theoretical maximum that could occur if everything were perfect. Remember, thermal efficiency is the network out divided by heat transfer in, and that can be on a specific basis or a magnitude or a rate of work and heat transfer. Since we're producing 300 kJ of network and consuming heat transfer at a rate of 700 kJ, that gives us a thermal efficiency of 3 7s, thank you calculator, of 0.428 or 42.86%. The theoretical maximum that could occur if everything were perfect comes from treating this heat engine as a Carnot heat engine, in which case our thermal efficiency is going to be 1 minus the low-side temperature divided by the high-side temperature, which is 1 minus 290 Kelvin divided by 500 Kelvin. And calculator says that represents a thermal efficiency of 0.2150, thank you calculator, of 42% on the nose. So we compare our thermal efficiency to the theoretical maximum and we see that our thermal efficiency is higher than the theoretical maximum. We are producing more work from this amount of heat transfer than is possible if there were no losses and everything were perfect. Therefore, this efficiency cannot occur, which means this is not a reasonable claim. Because it's not violating the first law, I mean, we don't know what the heat rejection is, we're not saying energy isn't conserved, we're just saying that we are converting energy with more efficiency than we can theoretically convert energy. Therefore, we are violating the second law.