(a) An ammonia vapour compression refrigeration system works between temperature limits of −6·7°C and 26·7°C. The vapour is dry at the end of compression and there is no under cooling of the liquid which is further throttled to the lower temperature.

Question

(a) An ammonia vapour compression refrigeration system works between temperature limits of −6·7°C and 26·7°C. The vapour is dry at the end of compression and there is no under cooling of the liquid which is further throttled to the lower temperature. Find the COP of the machine. Use the above properties of ammonia. (20 marks)

(b) In a cogeneration plant, steam enters the HP stage of a two-stage turbine at 1 MPa, 200°C and leaves it at 0·3 MPa. At this point some of the steam is bled off and passed through a heat exchanger which it leaves as saturated liquid at 0·3 MPa. The remaining steam expands in the LP stage of the turbine to 40 kPa. The turbine is required to produce a total power of 1 MW and the heat exchanger is required to provide a heating rate of 500 kW. Assuming all processes to be ideal, calculate the required mass flow rate of steam into the HP stage of the turbine.
(At 1 MPa, 200°C : h = 2827·9 kJ/kg and s = 6·6939 kJ/kg K)
Also use Steam Tables given at the end of the booklet. (20 marks)

(c) Compare the throttling processes happening at the following two locations in the steam power plant and using T-s diagrams contrast the observed phenomena :
(i) throttling of steam at inlet to turbine for governing.
(ii) throttling of condensate in closed feed heater trap exit. (10 marks)

UPSC Answer Check · Accepted Answer

Solve the three sub-parts sequentially, allocating approximately 40% time to part (a) COP calculation using ammonia properties, 40% to part (b) cogeneration mass flow rate with energy balance, and 20% to part (c) T-s diagram comparison of throttling processes. For each numerical part, state assumptions clearly, show property extraction from tables, and present final answers with units. For part (c), draw two distinct T-s diagrams with clear labelling of states and entropy changes.
- Part (a): Identify T1 = 266.3 K, T2 = 299.7 K; use h_f, h_g, s_f, s_g at given temperatures from ammonia tables; calculate h1, h2, h4 with dry compression and isentropic expansion assumptions; COP = (h1-h4)/(h2-h1)
- Part (b): Apply steady flow energy equation to HP turbine, heat exchanger, and LP turbine; use given h at 1 MPa, 200°C; find h at 0.3 MPa (saturated liquid for bleed, isentropic expansion for remaining steam to 40 kPa); set up simultaneous equations for power (1 MW) and heating (500 kW) to solve for mass flow rates
- Part (c)(i): Throttling at turbine inlet for governing — high pressure steam, large pressure drop, significant temperature drop, entropy increase, moves toward saturation, used for load control
- Part (c)(ii): Throttling at closed feed heater trap exit — saturated liquid at lower pressure, smaller enthalpy drop, minimal temperature change, entropy increase but different magnitude, used for condensate return
- Part (c): Two T-s diagrams showing: (i) superheated steam throttling with large Δs, moving closer to saturation line; (ii) subcooled/saturated liquid throttling with smaller Δs, remaining in liquid region or entering wet region slightly
- Correct use of steam table data: at 0.3 MPa, identify h_f for bleed condensate; for LP turbine exit, find quality or h at 40 kPa using s_2 = s_3 (isentropic)
- Mass balance: m_total = m_bleed + m_LP; energy balances: W_turbine = m_total*(h1-h2) + m_LP*(h2-h3); Q_heater = m_bleed*(h2-h_f at 0.3 MPa)

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly identifies reversed Carnot cycle limitations for part (a); recognizes cogeneration as combined heat and power with extraction turbine for part (b); distinguishes high-pressure steam throttling (governing, large Δh, entropy generation affects availability) from liquid throttling (trap, small Δh, flash potential) for part (c); uses correct thermodynamic relations h = constant for throttling, s = constant for isentropic expansion.	Uses correct basic formulas (COP, SFEE) but confuses throttling vs isentropic processes in one part; recognizes cogeneration concept but misapplies extraction turbine energy balance; T-s diagrams qualitatively correct but missing key distinctions.	Treats throttling as isentropic or reversible; confuses refrigeration COP with heat pump COP; fails to recognize extraction turbine configuration; draws incorrect T-s diagrams showing temperature increase during throttling.
Numerical accuracy	20%	10	Part (a): COP ≈ 4.5-5.0 with correct property interpolation; Part (b): mass flow rate ≈ 1.2-1.5 kg/s with consistent energy balances; all enthalpy values from tables correctly interpolated; arithmetic errors less than 2%; final answers with proper units and significant figures.	Correct methodology but one significant calculation error (e.g., wrong h4 in refrigeration cycle, or incorrect quality calculation in LP turbine); final answers within 10% of correct value; minor unit inconsistencies.	Multiple calculation errors; wrong property values (e.g., using saturated vapor instead of superheated at 1 MPa, 200°C); order of magnitude errors in mass flow rate; no units or incorrect units throughout.
Diagram quality	20%	10	Part (c): Two clear T-s diagrams with properly shaped saturation dome; diagram (i) shows superheated steam at state 1, horizontal throttling line to state 2 with increased entropy and reduced temperature, approaching saturation; diagram (ii) shows saturated/subcooled liquid throttling with smaller entropy increase, remaining in liquid region; both with state points labelled, constant pressure lines, and arrows indicating process direction; part (a) and (b) may include system schematics.	T-s diagrams present but missing labels or with incorrect process directions; one diagram correct, other confused; saturation dome poorly shaped; throttling lines not horizontal; missing constant pressure lines.	Single generic T-s diagram for both cases; or diagrams showing temperature increase during throttling; no diagrams for part (c); hand-drawn sketches illegible; confuses T-s with P-h or h-s diagrams.
Step-by-step derivation	20%	10	Part (a): Explicit statement of assumptions (dry compression, no undercooling, isentropic compression), property table lookup with interpolation shown, state-by-state enthalpy calculation, COP formula derivation; Part (b): Clear SFEE application to each component, simultaneous equation setup for m_total and m_bleed, algebraic solution shown; Part (c): Logical comparison structure with process equations (h1=h2, ds>0) for each case.	Key formulas stated but some intermediate steps skipped; property values stated without showing table reference or interpolation; energy balances correct but algebraic manipulation condensed; part (c) descriptive rather than equation-based.	Final answers only with no working; or incorrect formulas applied (e.g., using Q/W instead of refrigeration effect/work); no systematic approach to simultaneous equations in part (b); part (c) purely verbal with no thermodynamic basis.
Practical interpretation	20%	10	Part (a): Comments on actual COP vs Carnot COP, effect of wet compression, practical ammonia system considerations (toxicity, high pressure); Part (b): Discusses significance of power-to-heat ratio, typical cogeneration applications (Indian sugar mills, NTPC plants), effect of bleed pressure optimization; Part (c): Explains why governing throttling reduces cycle efficiency (availability destruction), while trap throttling is unavoidable but minimizes loss; mentions alternatives like nozzle governing vs throttle governing.	Brief mention of practical relevance for one part; generic statements about energy efficiency without specific context; recognizes cogeneration saves fuel but no quantitative or sector-specific insight.	No practical interpretation; treats all problems as pure academic exercises; no mention of real-world implications of throttling losses or cogeneration benefits; ignores Indian context entirely.

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