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Posted by on Jul 15, 2011 in Physical Chemistry | 0 comments

Simple Explanation of Thermodynamic Efficiency

Recall the following image (click to enlarge) from the post on the Thermodynamics of Heat Flow.  It contains a common sense definition of efficiency in its simplest terms.  That is, forget about noise, friction, sticky wheels and just ask the fundamental question: what is efficiency?

The hot reservoir contains the energy that we will use.  It has the potential to do work as we release it through an engine.  We have to pay for all that hot energy, so it figures into efficiency.  How much work can we get out of an engine (-w) for a given input of expensive energy, (qH)?

The more heat that is converted into work, the more efficient the process.  The heat lost to the cold reservoir cannot be recovered. Efficiency is therefore define as the ratio of work out to heat in,

In terms of symbols,

Note that the heat that flows into the system is positive, qH , and the work done on the surroundings is negative.  Hence if you put into an engine 1,000 Joules of energy and you get out 300 Joules of work, then the efficiency is 30%.  More “work out for less heat in” will increase the efficiency.

Notice that not all the heat is converted into work.  Some exits the engine and flows to the cold reservoir.  Hence the work is equal to the difference between the heat in and out,

This is, again, conservation of energy.

The study of efficiency led to the discovery of a new state function, entropy, a substance as tangible as energy.

A heat pump

A heat pump operates in reverse of an engine. Examples of heat pumps are refrigerators, air conditioners and heaters in the winter.  The following movie shows an idealized heat pump.


In this case work is put into the engine, (say a compressor) and this allows heat to be pumped up from the cold to the hot reservoir.  Hence your refrigerator is the cold reservoir and the hot one is outside the fridge (which is why you feel heat from the back of a fridge). The amount of heat that is removed from the outside and pumped into a house (-qH) is equal to the work done by the compressor (w) plus the work lost in the process (qC)

When using a heat pump to heat a house, heat is pumped from the outside cold into the house (the hot reservoir).  The colder it is outside, the harder it is to pump.  Note, however, that a heat pump is always more efficient than burning fuel to heat.  For example, if the temperature is 0 C (32 F) and the inside temperature is 21 C (70 F), for one kilowatt of work, it is possible to pump four kilowatts of heat. At -12 C (10 F), about 1.9 kilowats are pumped for the price of 1 kW.  Pumping energy  is cheaper than producing it.


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