# Why Even An Ideal Engine Cannot Have 100% Efficiency?

When we talk about ideal engines in Physics, we meant one in which there is no loss of energy because of dissipative forces like friction and viscosity. Ideal systems do not exist in the real world, because forces like friction cannot be removed completely, but even hypothetically, if we could indeed have an ideal engine, it would not be 100% efficient.

Efficiency is the measure of useful work or output obtained from an engine when some input energy is supplied to it through processes like mechanical work, and heat. To be mathematical, efficiency is the ratio of Output Work obtained from the engine to the Input Energy supplied to it.

When I say an engine, what I mean is a cyclic heat engine. In a layman’s term, cyclic engine is one which after taking in input, and doing work, returns to its initial conditions, and so is said to work in  a cycle. Heat engines comprises of a source of heat, a working material, and a sink, which is at a lower temperature than the source. The work is obtained through the working material, extracting heat from the reservoir, converting a part of it into work, and in the process loosing the remaining part to the sink. Now, according to Second Law of Thermodynamics, the Kelvin-Plank statement says that it is impossible to devise an engine, whose sole purpose is to extract heat from a body at higher temperature(reservoir) and convert the whole of it to equivalent work, without loosing a part of it to a sink(body at a lower temperature). Even if you remove all the heat loss through friction, the engine will lose a part of it to the surroundings, or the sink.

If Q is the amount of heat extracted from the source, and Q’ is the amount of it transferred to sink, the efficiency of a Carnot’s engine is found to be:

η = 1-(Q’/Q)

Since, the second law of thermodynamics clearly states that Q’ has to be a positive non-zero quantity, the efficiency is always less than 1 or 100%, even for a Carnot Engine[¹], which is an ideal, reversible engine, first hypothesized by Nicolas Léonard SadiCarnot in 1824.  No engine can be more efficient than  a carnot engine. (For proper working, see the link at the bottom)

This is also a consequence of entropy. Entropy is a measure of the amount of unavailable energy in the universe, or so as to say waste energy. The crucial point is, it always increases, it can never decrease. So, when heat is lost, it is actually energy that cannot be converted to useful work, and is thus unavailable energy. This increases entropy, and so, there HAS to be an amount of heat rejected to the sink.

So even speaking for science fiction, a heat engine that converts the whole amount of input energy to useful work is impossible, even if it’s an ideal one. It’s not an engineering problem, but restricted by the very laws of physics. Happy Reading!

-The Cosmogasmic Person