3.8: Overall Efficiency

Last updated
Save as PDF

Page ID: 48769

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Calculating Overall Efficiency

Using the energy efficiency concept, we can calculate the component and overall efficiency:

\[ Overall \, Efficiency = \dfrac{Electrical \, Energy \, Output}{Chemical \, Energy \, Input} \]

Here the electrical energy is given in Wh and Chemical Energy in BTUs. So Wh can be converted to BTUs knowing that there are 3.412 Wh in a BTU.

This overall efficiency can also be expressed in steps as follows:

\[ Overall \, Efficiency = \underbrace{ \left\lbrack \dfrac{Thermal \, Energy}{Chemical \, Energy} \right\rbrack }_{Boiler \, Efficiency} * \underbrace{ \left\lbrack \dfrac{Mechanical \, Energy}{Thermal \, Energy} \right\rbrack }_{Turbine \, Efficiency} * \underbrace{ \left\lbrack \dfrac{Electrical \, Energy}{Mechanical \, Energy} \right\rbrack }_{Generator \, Efficiency} \]

\[ OverallEfficiency = \eta_{boiler} * \eta_{turbine} * \eta_{generator} \]

Steps of Overall Efficiency

We have been looking at the efficiencies of an automobile or a power plant individually. But when the entire chain of energy transformations is considered—from the moment the coal is brought out to the surface to the moment the electricity turns into its final form—true overall efficiency of the energy utilization will be revealed. The final form at home could be light from a bulb or sound from a stereo. The series of steps are:

Production of coal (mining)
Transportation to power plant
Electricity generation
Transmission of electricity
Conversion of electricity into light (use)

The following video discusses overall power plant efficiency.

Efficiency of a Light Bulb

If efficiency of each step is known, we can calculate the overall efficiency of production of light from coal in the ground. Table 3.8.1 illustrates the calculation of overall efficiency of a light bulb.

Table 3.8.1. Calculation of overall efficiency of a light bulb

Step	Step Efficiency	Cumulative (Overall) Efficiency
Extraction of coal	96%	96%
Transportation	98%	94% = (0.96 * 0.98) * 100%
Electricity generation	35%	33% = (0.94 * 0.35) * 100%
Transmission of electricity	95%	31% = (0.33 * 0.95) * 100%
Lighting: incandescent bulb	5%	1.56% = (0.31 * 0.05) * 100%
Lighting: fluorescent bulb	20%	6.2% = (0.31 * 0.20) * 100%

Efficiency of an Automobile

A similar analysis on automobile efficiency is shown in Figure 3.8.1.

Figure 3.8.1. Overall automobile efficiency

Table 3.8.2 shows that only about 10% of the energy in the crude oil in the ground is in fact turned into mechanical energy moving people.

Table 3.8.2. Automobile efficiency

Step	Step Efficiency	Cumulative/Overall Efficiency
Extraction of crude oil	96%	96%
Refining	87%	84%
Transportation	97%	81%
Engine	25%	20%
Transmission	50%	10%