Set 54 Problem number 19

Problem

A thermal engine takes in 810 Joules of thermal energy, and 761.4 Joules of thermal energy are removed or dissipated during a cycle.    What is the efficiency of the engine?

Solution

If 810 Joules of thermal energy are put into the system and 761.4 Joules are wasted, then the difference

• difference between thermal energy in and thermal energy wasted: 810 J - 761.4 J = 48.59998 J

is the work done by the system.

Efficiency is work done divided by energy input, or

• efficiency: 48.59998 J / ( 810 J) = 5.999997E-02 .

Generalized Solution

Efficiency is a fairly natural idea: what you get divided by what you put in. In this case we put energy into the system and take out or lose somewhat less energy during cooling and other processes; the difference between what goes in and what is taken out or lost is the work done by the system.

If we denote the energy put into the system as Qin and the energy taken out or lost as Qout, then conservation of energy requires that Qin = work done by system + Qout. If we denote the work done by the system by W, then we see that

W = Qin - Qout.

The efficiency of the process is therefore

efficiency = work done / energy in = W / Qin = (Qin - Qout) / Qin.

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