Question

efficiency of an engine is less than 100% why?

Answer 1

In a Carnot’s engine an ideal gas enclosed within a cylinder fitted with a piston which is is first isothermally expanded by letting some heat flow from the source, then it is adiabatically compressed where no heat is exchanged with the surrounding. After adiabatic compression the system is kept in the sink and is allowed to expand isothermally where it gives off a part of heat to the sink. Then the system is again compressed adiabatically. This adiabatic compression brings the system back to the initial state.
Let Q1 amount of heat be taken from the source at temperature T1
Let Q2 amount of heat be expelled from the system to the sink kept at temperature T2.
Thus work done by the engine must be equal to W = Q1 – Q2
Now the efficiency of the engine η = Work done /Input heat
Thus η = (Q1 – Q2)/Q1 = 1 – Q2/Q1
Now Q2­ = ST2 and Q1 = ST1 Where S = entropy of the engine (assumed to be constant)
=> η = 1 – T2/T1 = (T1 – T2 )/T1
Since, the numerator here is always less than the denominator, η is always less than 1. Hence, the efficiency is never 100%.