Compression ratio and engine efficiency. The Otto cycle shown in Figure P16.61 is the id...

Compression ratio and engine efficiency. The Otto cycle shown in Figure P16.61 is the idealized cycle for an internal combustion automobile engine. Corresponding to positions of the piston, the cycle is in four parts (two isochoric and two adiabatic). (a) Show that Equation 16.19 describing the efficiency can be expressed as for the Otto cycle, where the temperatures are taken from the four points on the cycle. (b) If an ideal gas is used as the working fluid, it turns out that the efficiency for the Otto cycle is independent of the temperature and depends only on the ratio called the compression ratio. Show that the efficiency can also be written in terms of the initial and final volumes as where for an ideal gas. Hint: Use the ideal gas law and Equation 16.10 to write each temperature in terms of volume and pressure.

(reference equation 16.10)