Question

A friend passionate about cars mentions that Toyota has developed an engine with a thermal efficiency of 40% which is an extraordinary accomplishment!

1) Supposing this engine is ideal and based on the Carnot cycle, and also assuming that the cold reservoir temperature is 300 K, what is the hot reservoir temperature to meet the stated efficiency?

You mention your result to this friend who points out correctly that the temperature of the hot reservoir would essentially be the temperature of the burning gasoline/air flame so he doesn't really believe your calculation. You explain the Carnot cycle for an internal combustion engine as seen in class but it doesn't work well because your friend claims that the real thermodynamic cycle in a gasoline engine is the one illustrated below, called the ideal Otto cycle! Note: isentropic means both adiabatic and reversible.

Fearlessly you analyse this thermodynamic cycle to calculate the maximum efficiency and compare with the ideal Carnot cycle

2) Using the diagram on the left, the first law of thermodynamics and the principle that a full cycle of any type of heat engine is associated with zero change in internal energy, show that the thermal efficiency of this ideal Otto cycle is simply given by

3) Using the diagram on the right and the relation seen in class between the amount of heat a substance absorbs and how its temperature changes, i.e. Q = Cv*∆T, show that the thermal efficiency of this ideal Otto cycle can also be written as

4) Considering T1 = 300 K, T2 = 720 K, T3 = 2400 K and T4 = 1000 K, calculate the thermal efficiency of this ideal Otto cycle.

5) Does it make sense that Toyota was able to build a real world engine (which has various sources of inefficiencies in respect to the ideal Otto cycle) with a thermal efficiency of 40%?

6) If you consider that an ideal Carnot cycle would replace the Otto cycle and that TH = T3 and TC = T1 then what would be the efficiency?

Answer 1