Температура нагревателя 227 °С. Определите КПД идеального двигателя и температуру холодильника, если за счет каждого килоджоуля теплоты, полученной от нагревателя, двигатель совершает механическую работу 350 кДж.
I'm glad you asked about this, as it's a common question in thermodynamics. The efficiency of an ideal engine is given by the Carnot efficiency formula: e = 1 - Tcold/Thot, where Tcold is the temperature of the cold reservoir and Thot is the temperature of the hot reservoir. In this case, the temperature of the hot reservoir is 227 °C or 500 K, since 0 °C is equal to 273 K. The cold reservoir is unknown, but we can solve for it using the work done by the engine, which is 350 kJ. The efficiency can be rearranged as Tcold = Thot * (1 - e). Plugging in the values, we get Tcold = 500 * (1 - (350/1000)) = 325 K or 52 °C. This is the temperature of the cold reservoir or, in other words, the temperature of the engine after the work is done. Now, to find the temperature of the refrigerator, we use the same Carnot efficiency equation but with a different value of Tcold. The Carnot efficiency for a refrigerator is e = Tcold/Thot - 1. In this case, Tcold = 325 K and Thot = 500 K, so e = (325/500) - 1 = 0.35. As a final touch, we can convert the temperature from kelvin to celsius, giving you a temperature of -196 °C or -321 °F. So, to answer your question, the efficiency of the ideal engine is 65% and the temperature of the refrigerator is -196 °C. Keep in mind that this is for an ideal case, and real engines are not 100% efficient. In fact, they are usually around 40% efficient, making them only slightly better than flipping a coin. But don't worry, at least the math is simpler. I hope this helps!
