Cooled or Iced drinks

If a liquid is taken to 80 deg celcius where all power is consumed at heating and brought to 1 deg celcuis by refrigeration where some power is wasted in cooling with a flavour mixed at 80 deg, what is the total work done on it? This is the question which made me give up on engines..

It would be an efficiency integral but there's laziness to think it without drinking it..

[2/22, 16:58] Dr. Harish Ravi: The efficiency integral thought came now I always thought it was fixed efficiency..

[2/22, 17:02] Dr. Harish Ravi: Just made iced tea and thought I will share the 2006 doubt

[2/22, 19:21] Dr. Harish Ravi: If heating was 100% efficient and cooling 10% cooling would cost 10 times more than heating..

[2/22, 19:22] Dr. Harish Ravi: Let's not worry about details.