A heat engine receives heat from a source at 1200 K at the rate of 500 kW and rejects the waste heat to a medium at 300 K. The power output of the heat engine is 180 kW. What will be the irreversibility of the system?

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SJVN ET Mechanical 2019 Official Paper

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Answer 1

Concept:

Irreversibility (or lost work) is defined as the difference between the reversible work output and the actual work output:

\( I = W_{rev} - W_{actual} \)

Reversible work is calculated using Carnot efficiency:

\( \eta_{rev} = 1 - \frac{T_2}{T_1} \)

Given:

Heat supplied, \( Q_1 = 500~\text{kW} \)

Source temperature, \( T_1 = 1200~\text{K} \)

Sink temperature, \( T_2 = 300~\text{K} \)

Actual work output, \( W_{actual} = 180~\text{kW} \)

Calculation:

\( \eta_{rev} = 1 - \frac{300}{1200} = 0.75 \)

\( W_{rev} = 0.75 \cdot 500 = 375~\text{kW} \)

\( I = 375 - 180 = 195~\text{kW} \)