UPSC Civil Services (Mains), Chemistry optional · 2025 · Paper I
Q1(j). Maximum work of a steam turbine
Question
A steam turbine is operated with an intake temperature of 400 °C, and an exhaust temperature of 150 °C. What is the maximum amount of work the turbine can do for a given heat input ‘Q’? Under what conditions is the maximum work achieved?
Answer in brief
wmax = 0.371 Q (37.1 % of the heat taken in), reached only when every step is reversible.
Key points
- The second law does not allow all of Q to become work; the largest work comes from a reversible (Carnot) engine between the same two temperatures.
- η = wmax/Q = 1 − Tc/Th = 1 − 423 K/673 K = 0.371, so wmax = 0.371 Q and 0.629 Q must leave at 150 °C.
- Conditions: heat taken in isothermally at 673 K and rejected isothermally at 423 K, with frictionless adiabatic expansion and compression in between, so that ΔSuniv = 0.
- A real turbine gives less, because friction and heat flow across a finite temperature difference create entropy.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
CoversCarnot cycleCarnot efficiencysecond law of thermodynamicsheat enginereversible process
All parts of Question 1
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- 1(j) Maximum work of a steam turbine5 marks