[Thermodynamics] Cooling intake air of an Otto cycle-engine AskPhysics

For a homework problem I have calculated the efficiency of an Otto cycle engine at T=0^C and T=20^C . For zero degrees, this gives an efficiency of 0.46 and for twenty degrees the efficiency is 0.42.

The follow-up question asks if it would be smart to add an ideal air conditioner that cools the incoming air to zero degrees before compression and to show why or why not with a calculation.

I have used the specific heat of air to calculate that it would take 14360 J/kg to cool air from 20 to 0 degrees. Taking an ideal refrigerator, the requested change in temperature gives a coefficient of performance of 14.65. Thus it would cost 980 J of net work to cool each kilogram of air.

Now I want to show what the new efficiency is taking this work into account. This would give something like e = (W - 980)/Q_h and answer should be higher or lower than 0.42. How can I get to this answer?

Submitted December 06, 2017 at 08:04PM by supercooldragons http://ift.tt/2AvvAQd AskPhysics