# Thermal Efficiency of a Power Cycle

## Thermal Efficiency

: η
a measure of the performance of a

#### power cycle

.
First Law :
For power cycles:
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### Ch 4, Lesson F, Page 6 - Thermal Efficiency of a Power Cycle

• Thermal efficiency is a measure of the performance of a power cycle or heat engine.
• The symbol for thermal efficiency is the Greek letter “ETA”, η.  It is a lower case “h” in the Symbol font if you ever need to type it.
• The thermal efficiency is defined as the ratio of the desire output of the cycle to the required input for the cycle.
• The goal of the power cycle is to produce a net amount of work, WHE, so this goes in the numerator when we want to calculate η.
• The required input is QH, so QH goes in the denominator.
• So, η = WHE divided by QH.
• We could leave it at that, but we can use the 1st Law to simplify this equation a bit further.
• If we substitute QH minus QC for WHE and then divide the numerator and denominator by QH, we get a clean little equation for calculating the thermal efficiency of a power cycle.
• η = 1 – QC/QH.  That equation isn’t too nasty.
• Let’s think about what this equation means for a second.
• If the heat engine could convert ALL of the heat that was input into work then QC would be zero and the thermal efficiency would be 1.
• We’ll see in Chapter 6 that this is not possible, but the higher the thermal efficiency, the more work you get out of the heat engine for each Joule you put into it in the form of QH and the less heat you have to waste by rejecting it in the form of QC.
• Cool.  So, now we have a clear way to compare one heat engine to another.
• Now let’s take a look at refrigeration cycles.