$(2)$ An ideal Otto cycle with air as the working fluid has a compression ratio of $8.$ The minimum and maximum temperatures in the cycle are $540$ and $2200$R$.$ Accounting for the variation of specific heats with temperature, determine a$)$ the anount of heat transferred to the air dwing the heat addition process, b$)$ the thermal efficiency,

c$)$ the thermal efficiency of a Carnot cycle operating between the same temperatures