Question

In a gas turbine plant, heat supplied is 667.2 kJ/kg, and heat rejected is 391.43 kJ/kg. What is the thermal efficiency of the plant?
1. 57.29%
2. 72.51%
3. 41.33%
4. 32.83%

Answer 1

Correct Answer - Option 3 : 41.33%

Concept:

Thermal efficiency:

\(\eta_{thermal} = \frac{Work~output}{Heat~input}=\frac{W}{Q_1}\)

\(\eta_{thermal} =\frac{W}{Q_1}\Rightarrow \frac{{Q_1}\;-\;{Q_2}}{Q_1}=1-\frac{Q_2}{Q_1}\)

where Q₁ = heat input and Q₂ = heat rejected.

Calculation:

Given:

Heat supplied Q1 = 667.2 kJ/kg, and heat rejected Q2 = 391.43 kJ/kg.

Thermal efficiency:

\(\eta_{thermal} =\frac{W}{Q_1}\Rightarrow \frac{{Q_1}\;-\;{Q_2}}{Q_1}=1-\frac{Q_2}{Q_1}\)

\(\eta_{thermal} =1-\frac{391.43}{667.2}\)

\(\eta_{thermal} =41.33\;\%\)