# The higher power requirements for compression in a steam power plant working on Carnot vapour cycle

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## Options:

1. Increases the plant efficiency as well as work ratio

2. Reduces the plant efficiency as well as work ratio

3. Does not affect the plant efficiency as well as work ratio

4. Increases the plant efficiency and reduces work ratio

### Correct Answer: Option 2 (Solution Below)

This question was previously asked in

ESE Mechanical 2020 Official Paper

## Solution:

Concept:

Plant Efficiency is the ratio of output power of turbine to the heat supplied to combustion and it is given as, $$\eta = \frac{{shaft\;work\;}}{{heat\;supplied\;}}$$

where, shaft work, Wnet = WT - WC and heat supply = Qs

Therefore, $$\eta = \frac{{{W_T} - {W_C}}}{{\;{Q_S}}}$$

where, WT = turbine work, WC = compressor work

If we use higher power compressor it will decrease net work (Difference between WT and WC decreases). So cycle efficiency will be decrease as compressor input power increases. and

Work ratio is defined as the ratio of net work output to turbine work

$${WR} = \frac{{Net\;work\;output,\left( {{W_{net}}} \right)}}{{Turbine\;work,\left( {{W_T}} \right)}}$$

⇒ $${WR} = \frac{{{W_T} - {W_C}}}{{{W_T}}}$$

As net work output deceases (Difference between WT and WC decreases) by increasing compressor power input. So work ratio also decreases due use of higher requirements for compression.

Back work ratio is the ratio of Compressor work to the Turbine work.

BWR = $$\frac{W_C}{W_T}$$ = 1 - WR
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