What is a heat engine? Explain the efficiency of a heat engine.

Explanation

A heat engine is a device that converts part of heat absorbed into work. It extracts energy in the form of heat from a heat source and does useful work as it continuously repeats a thermodynamic cycle, discarding some heat to a heat sink.
To convert heat into work on a sustained basis in a heat engine, a working substance is repeatedly taken through the same thermodynamic cycle. The net work delivered to the outside is called the output, and the heat absorbed by the working substance is called the input.
The thermal efficiency (or simply efficiency) `(eta)` of the engine is defined as
`eta=("work output")/("heat input")` (in one cycle)
with both work and heat expressed in the same unit.
In one cycle, let `Q_h` be the energy absorbed as heat by the working substance from a hot reservoir `("constant temperature T_h), Q_c` be the energy discharged or rejected as heat by the working substance to a cold reservol or sink (a heat reservoir at constant temperature `T_c lt T_h`), and W be the work output.
There is no net change in the internal energy as the working substance completes the cycle, returning to the initial state.
Applying the first law of thermodynamics, dQ=dE+dW, we have ` triangleQ=triangleE+W=0+W` on completion of a cycle.
`therefore Q_h-Q_c=W`
In one cycle, let Q, be the energy absorbed as heat by the working substance from a hot reservoir (constant temperature T), `Q_c` be the energy discharged or rejected as heat by the working substance to a cold reservol or sink (a heat reservoir at constant temperature `T_(c) lt T_(h))`, and W be the work output.
There is no net change in the internal energy as the working substance completes the cycle, returning to the initial state.
Applying the first law of thermodynamics, dQ=dE+dW, we have on completion of a cycle.
`triangleQ` = `triangleE`+ W=0+ W on completion of a cycle `thereforeQ_h-Q_c=W` `therefore eta=(W)/(Q_h)=(Q_h-Q_c)/(Q_h)=1-(Q_c)/(Q_h)`
`eta` is always less than 1 (i.e., less than 100%) as Q. is always less than `Q_h`