Bluffton University

NSC111: Physics/Earth/Space
Resource page: Thermodynamics

V. Heat engines can never operate at 100% efficiency

A heat engine has three components:
  1. The Hot Reservoir (or Heat Source).
  2. The Cold Object or Heat Sink.
  3. The object on which Work is done.
diagram of a heat engine

According to the First Law of Thermodynamics,

In an isolated system,
the total amount of energy is conserved.

We observe in the laboratory that:

  1. For heat to flow from a source to a sink, there must be a temperature difference.
  2. When heat is transferred from one body to another, the temperatures equalize. As the temperature of the heat source falls, that of the heat sink rises.
  3. When temperatures are equal, no more heat can be transferred, even though the hot and cold objects still contain heat.
Thus, heat transferred from a heat source to a sink is used to raise the temperature of the sink while that of the source falls, until the temperatures are equal and no more heat can be transferred.

We also notice that when we melt ice, the temperature of the hot water falls but the temperature of the ice does not rise until it is all melted. This can be generalized to say that

  1. When heat is converted into work, the temperature of the heat source falls, approaching that of the heat sink. (This follows from conservation of energy.)
diagram of a heat engine But as the temperature of the heat source falls, it approaches the temperature of the heat sink until the temperatures are equal. This means that no more heat can be transferred, and since we are getting work from heat transfer,
  1. If there is no temperature difference, no heat can be converted into work. But if there is a temperature difference, some of the heat will be used to raise the temperature of the heat sink.
Furthermore, if work is being done by the heat engine, the object on which work is being done is not isolated from the heat engine. Unless it is at the same temperature as the heat source, heat will flow in a conventional manner from the heat source to the object on which work is being done, and the object's temperature will rise.
If the object is at the same temperature as the heat source, no work can be done on it unless heat is flowing from heat source to the heat sink. This is a consequence of point (5).
But
  1. If some of the heat must go into raising the temperature of a sink, not all of it can be converted into work.
It doesn't matter whether the sink is labeled "heat sink" or "object on which work is being done". This leads us to conclude

It is not possible to construct an engine which
does nothing but convert heat into useful work.

The maximum (or "theoretical") efficiency of any heat engine is described in terms of the temperatures of the heat source and heat sink. Temperatures are expressed in the Kelvin scale (Celsius + 273).

Theoretical Efficiency =  Thot - Tcold  ×100%
Thot

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Copyright © 2001 by Daniel J. Berger. This work may be copied without limit if its use is to be for non-profit educational purposes. Such copies may be by any method, present or future. The author requests only that this statement accompany all such copies. All rights to publication for profit are retained by the author.