Problem 1: Otto cycle Prove directly (by calculating the heat taken in and the heat expelled) that an Otto engine using an ideal gas as the working substance has an efficiency of e = 1 –

Suppose a heat engine design makes a square on a PV diagram, using a monatomic gas. The high pressure is 3P and low pressure is P. The high volume is 3V and low volume is V. What is the efficiency of the heat engine?

a) A thermal engine operates between reservoirs of 280K and 370K. Compute its maximum thermal efficiency. b) A refrigerator operates between reservoirs of the 290K and 370K. What would the temperature of the hot reservoir need to be in order to double its coefficient of performance, assuming it was operating as a Carnot cycle? C) A Carnot engine is operating with a cold reservoir at 290K. What temperature is required for the hot reservoir in order that the engine has an efficiency of 30% ? d) Each cycle, a refrigerator passes 150J to the hot reservoir while doing 71J work. What is its coefficient of performance?