Question

The efficiency of an internal combustion engine is given by E= (1-v/V)^0.4
Where V and v are the respective maximum and minimum volumes of air in each cylinder.
a) Show that ∂E/ ∂V > 0 and interpret your result
b) Show that ∂E/ ∂v < 0 and interpret your result

Answer 1

I assume you can do the partial derivatives.

V represents the maximum volume, which is most probably related to the external size of the cylinder. Do you expect a better efficiency with a bigger cylinder?

v represents the "dead" volume of the cylinder. Increase of v means decrease of the active volume, V-v. Think of its effect on the efficiency.