As a gasoline engine is running, an amount of gasoline containing 15,000J of chemical potential energy is burned in 1 s. During that second, the engine does 3,000 J of work. (b) The burning gasoline has a temperature of about 2500 K. The waste heat from the engine flows into air at about 300 K. What is the Carnot efficiency of a heat engine operating between these two temperatures

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Explanation:

The Carnot efficiency is the maximum theoretical efficiency that a thermal machine can reach, the expression is:

The real efficiency of the engine is:

Real efficiency of the engine must be lower than maximum theoretical efficiency due to irreversibilities.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west