UPSC Civil Services (Main) Examination 2026 — Mechanical Engineering Optional Paper II: Question Paper | Plutus IAS

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09 Sep UPSC Civil Services (Main) Examination 2026 — Mechanical Engineering Optional Paper II: Question Paper | Plutus IAS

Posted at 09 Sep 2026 in UPSC by
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The questions below are from Mechanical Engineering Optional Paper II of UPSC Civil Services (Main) Examination 2026 (held 2026-08-30) — the actual paper, which is public government content. This page carries the questions for reference and revision; model answers for this paper are not published here.

Official paper (PDF): upsc.gov.in.

  1. (a) A piston-cylinder contains $2 \text{ kg}$ of argon at $T_1 = 300 \text{ K}$ and $V_1 = 1 \text{ m}^3$ (state 1). Argon is heated by an electric heater of $10 \text{ A}$, $220$ volts for $10$ seconds at constant volume; during the process, $20\%$ heat is lost (state 2). The gas is now allowed to expand from pressure $P_2$ to a final state with temperature $T_3 = 40 \text{ °C}$ and final pressure $P_3 = 0.5P_2$ (state 3). The process 2-3 follows $PV^n =$ constant. Find the index of expansion $n$ for the process 2-3. Take for argon $R = 0.2081 \text{ kJ/kg-K}$ and $C_v = 0.312 \text{ kJ/kg-K}$. (b) A gas turbine plant operates on ideal Brayton cycle between $T_{\text{min}} = 300 \text{ K}$ and $T_{\text{max}} = 1200 \text{ K}$. Find the maximum work done per kg of air and the corresponding cycle efficiency. Assume $C_p$ of air as $1.005 \text{ kJ/kg-K}$. (c) An air jet ($\gamma = 1.4$, $R = 287 \text{ J/kg-K}$) at $425 \text{ K}$ has sonic velocity. Determine the (i) velocity of sound at the stagnation condition, (ii) maximum velocity of the jet and (iii) Crocco number. (d) ![img-0.jpeg](img-0.jpeg) Determine the heat transfer through the composite wall shown in the figure below. Take the thermal conductivities of A, B, C, D and E as 50, 10, 8, 20 and 25 W/m-K, respectively and assume one-dimensional heat transfer : ![img-1.jpeg](img-1.jpeg) (e) Consider a large plane wall of thickness 0.25 m, having thermal conductivity 3 W/m-°C and surface area 10 m$^{2}$. The left side of the wall is subjected to a net heat flux of 750 W/m$^{2}$. The surface temperature of the left side of the wall is 90 °C. Assuming constant thermal conductivity and no heat generation in the wall, express the differential equation and boundary conditions for steady one-dimensional heat conduction through the wall. Also, obtain a relation for the variation of temperature in the wall by solving the differential equation and find the temperature of the right side of the wall. (1) brake thermal efficiency;
  2. (a) During a heat transfer process, the entropy change of incompressible substances, such as water, can be determined from $$\Delta S = mC_{\text{avg}} \ln \left( \frac{T_2}{T_1} \right)$$ . Show that for thermal energy reservoirs, such as large lakes, this relation reduces to $$\Delta S = \frac{Q}{T}$$ . A refrigeration system is to cool bread loaves with an average mass of 400 g from 25 °C to -10 °C at a rate of 400 loaves per hour by refrigerated air at -25 °C. Taking the average specific and latent heats of bread to be 2.90 kJ/kg-°C and 109.15 kJ/kg, respectively, determine (1) the rate of heat removal from the bread in kJ/hr and (2) the required volume flow rate of air in m³/hr, if the temperature rise of air is not to exceed 5 °C. The gas constant of air is 0.287 kPa·m³/kg-K. The specific heat of air at average temperature is 1.0 kJ/kg-°C. Take atmospheric air pressure as 101.3 kPa. (b) Show that the entropy change across the normal shock in an adiabatic flow in a duct is given by $$\Delta S = -R \ln \left( \frac{P_{0Y}}{P_{0X}} \right)$$. Differentiate between Fanno and Rayleigh flows. (c) $$\begin{array}{l} k = 0.0248 \text{ W/m-}^\circ\text{C} \\ v = 1.412 \times 10^{-5} \text{ m}^2/\text{s} \\ \text{Pr} = 0.72 \end{array}$$ $$\text{Nu} = (0.037 \text{ Re}^{0.8} – 871) \text{ Pr}^{0.33}$$ Wind is blowing at 50 km/hr along a 12 m long and 5 m high wall of a house. The atmospheric air is at 4 °C and the wall surface temperature is 10 °C. Determine the rate of heat loss from the wall by convection. The properties of air at 1 atmosphere and at mean film temperature may be taken as : $$\begin{array}{l} k = 0.0248 \text{ W/m-}^\circ\text{C} \\ v = 1.412 \times 10^{-5} \text{ m}^2/\text{s} \\ \text{Pr} = 0.72 \end{array}$$ Use the Nusselt number correlation for combined flow : $$\text{Nu} = (0.037 \text{ Re}^{0.8} – 871) \text{ Pr}^{0.33}$$ (2) indicated thermal efficiency;
  3. (a) $$\begin{array}{l} \rho = 998.8 \text{ kg/m}^3 \\ C_p = 4184.5 \text{ J/kg-}^\circ\text{C} \\ h_{fg} (\text{जल}) = 2406 \text{ kJ/kg} \end{array}$$ Steam at 40 °C is condensed in a power plant using cooling water available at 12 °C. The flow rate of steam is 0.15 kg/s. The cooling water is circulated through a bank of 6 m long and 1.25 cm internal diameter thin copper tubes at a mean velocity of 3.5 m/s, and leaves at a temperature of 20 °C. The tubes are nearly isothermal at 40 °C. Calculate the average heat transfer coefficient between the water and the tubes, and find the number of tubes needed to achieve the indicated heat transfer rate in the condenser. The properties of water at an average temperature may be taken as : $$\begin{array}{l} \rho = 998.8 \text{ kg/m}^3 \\ C_p = 4184.5 \text{ J/kg-}^\circ\text{C} \\ h_{fg} (\text{water}) = 2406 \text{ kJ/kg} \end{array}$$ (b) The mean diameter of the rotor of an axial flow compressor is 0.5 m, and it rotates at 15000 r.p.m. The flow velocity is 220 m/s and is constant. The velocity of whirl at the inlet is 80 m/s. The inlet pressure and temperature are 1 bar and 300 K, respectively. The stage efficiency is 0.88. The pressure ratio through the stage is 1.5. Draw the velocity triangles and determine the (i) blade angles at inlet and outlet, (ii) power input and (iii) degree of reaction. Take ratio of specific heats for air = 1.4 and $C_p = 1.005 \text{ kJ/kg-K}$. (c) [ P.T.O. Thin square plates of size 2.5 m × 2.5 m are coming out of an oven at 280 °C in a material processing facility. The plates are cooled by blowing ambient air at 20 °C horizontally parallel to their surfaces. Determine the air velocity above which the natural convection effects on heat transfer are less than 12% and thus are negligible. The kinematic viscosity of air at 1 atmosphere may be taken as v = 2.859 × 10⁻⁵ m²/s. (3) indicated mean effective pressure;
  4. (a) The air-fuel ratio of an SI engine varies under different operating conditions. Write the air-fuel ratio requirement for an engine under the following conditions with reasons : – (i) Idling or no-load condition – (ii) Cruising or part-load condition – (iii) Maximum power or full-load condition (b) What are the functions of lubricant used in IC engines? Mention the essential properties of IC engine lubricant. (c) Describe the behaviour of steam flow in a convergent nozzle when it is operated at— – (i) design pressure ratio; – (ii) pressure ratio higher than the design value; – (iii) pressure ratio lower than the design value. (d) List the deviations that occur in a compression process in actual vapour compression refrigeration cycle in comparison to simple saturated vapour compression refrigeration cycle. Also, specify the reasons for these deviations. (e) What is the difference between room ADP and coil ADP? Under which condition, both will have the same value?
  5. (a) In an Otto cycle, the pressure and temperature at the beginning of compression are 1 bar and 47 °C, respectively. Calculate the theoretical thermal efficiency of this cycle, if the pressure at the end of the compression is 15 bar. The peak temperature during the cycle is 2100 K. Calculate— (i) the heat supplied per kg of air; (ii) the work done per kg of air; (iii) the pressure at the end of expansion. Take $$C_v = 0.717 \text{ kJ/kg-K}$$ and $$\gamma = 1.4$$. (b) A single-row impulse steam turbine with a blade speed of 200 m/s and mass flow rate of 4 kg/s develops 300 kW of power. Steam leaves the nozzle at 500 m/s and the blade velocity coefficient is 0.92. If the steam leaves the turbine at such an angle that the exit absolute velocity is kept minimum, determine all the angles and diagram efficiency. Draw compound velocity triangles. (c) "The COP of a simple vapour absorption refrigeration system is lower than the COP of a simple vapour compression refrigeration system under identical temperature conditions." Is this statement correct thermodynamically? Justify your answer. [ P.T.O.
  6. (a) In a cogeneration plant, the net power output is 6 MW and the heating load is 1.5 MW. Steam is generated at 40 bar and 500 °C, and is expanded isentropically through a turbine to a condenser at 0.1 bar. The heating load is supplied by extracting steam from the turbine at 2 bar, which is condensed in a process heater to saturated liquid at 2 bar and then pumped back to the boiler. Draw the schematic and T-s diagram. Determine (i) the steam generation capacity (in kg/s) of the boiler and (ii) mass flow rate (in kg/s) of the steam through the heating load. The steam properties at 40 bar, 500 °C are h = 3445.21 kJ/kg, s = 7.09 kJ/kg-K. Use steam tables given at the end to get other properties. (b) | — | — | — | — | — | | -16 | 126.73 | 1442.60 | 0.72511 | 5.8420 | | 40 | 390.59 | 1490.42 | 1.64377 | 5.1558 | An R717 simple saturation cycle refrigerator operates at 40 °C condenser and -16 °C evaporator temperatures. Determine COP and power per TR. If a liquid-vapour regenerative heat exchanger is installed in the system, with the suction vapour at 15 °C, what will be the effect on COP and power per TR? Assume specific heat of vapour at condenser temperature as 3.1 kJ/kg-K, when no heat exchanger is used, and 2.9 kJ/kg-K, when heat exchanger is used. The properties of R717 are given in the table below : | Temperature (°C) | Enthalpy (kJ/kg) | | Entropy (kJ/kg-K) | | | — | — | — | — | — | | | Liquid (h_{f}) | Vapour (h_{g}) | Liquid (s_{f}) | Vapour (s_{g}) | | -16 | 126.73 | 1442.60 | 0.72511 | 5.8420 | | 40 | 390.59 | 1490.42 | 1.64377 | 5.1558 | Draw the P-h diagram also. The specific heat of vapour corresponding to evaporator temperature may be assumed as 2.38 kJ/kg-K. (c) How are the ratings of SI and CI engine fuels done? Explain in brief.
  7. (a) An air-conditioned space is maintained at 25 °C DBT and 50% RH. The outside conditions are 40 °C DBT and 27 °C WBT. The space has a sensible heat gain of 24.5 kW. Conditioned air is supplied to the space as saturated air at 10 °C. The equipment consists of an air washer. The air entering the air washer comprises 25% of outside air, the remainder being recirculated room air. Calculate the— (i) volume flow rate of air supplied to space; (ii) room sensible heat factor; (iii) cooling load (in TR) of air washer. Psychrometric chart is given at the end. Also, draw the schematic diagram and show the various processes on a skeleton psychrometric chart. (b) Describe the method of finding indicated power of an IC engine using Morse test.

Questions reproduced from the official paper for study purposes; verify on the exam-conducting body’s official website.

Related — other papers of this exam

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