A system consisting of a cylinder full of gas, sealed by a piston, is alternately loaded, heated, unloaded and then cooled back to its original state. If heating requires 950 Joules and if 560.5 Joules of thermal energy are taken out or lost during cooling and other processes, then what is the efficiency of the system?
If 950 Joules of thermal energy are put into the system and 560.5 Joules are wasted, then the difference
is the work done by the system.
Efficiency is work done divided by energy input, or
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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