ME-302 Thermodynamics - Dec 2024 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aWhat is thermodynamics equilibrium? Explain mechanical, chemical and thermal equilibrium.
   How to answer

   • Definition of thermodynamic equilibrium (simultaneous existence of thermal, mechanical, and chemical equilibrium)
   • Explanation of thermal equilibrium (uniformity of temperature, no heat transfer)
   • Explanation of mechanical equilibrium (balance of forces, uniform pressure, no work transfer)
   • Explanation of chemical equilibrium (no chemical reaction, uniform chemical potential)
2. 7 Marks
   bIn an air motor cylinder the compressed air has an internal energy of $450\text{ kJ/kg}$ at the beginning of the expansion and an internal energy of $220\text{ kJ/kg}$ after expansion. If the work done by the air during the expansion is $120\text{ kJ/kg}$, calculate the heat flow to and from the cylinder.
   How to answer

   • State First Law of Thermodynamics for a closed system: $q - w = \Delta u$
   • Calculate change in internal energy: $\Delta u = u_2 - u_1 = 220 - 450 = -230\text{ kJ/kg}$
   • Calculate heat transfer: $q = \Delta u + w = -230 + 120 = -110\text{ kJ/kg}$
   • Conclude that $110\text{ kJ/kg}$ of heat is rejected from the cylinder
3. 7 Marks
   aGive Kelvin Plank's and Clausius statements for the second law of thermodynamics.
   How to answer

   • Kelvin-Planck Statement: Impossibility of a heat engine operating in a cycle to produce work while exchanging heat with a single reservoir
   • Schematic representation of Kelvin-Planck statement violation (PMM2)
   • Clausius Statement: Impossibility of transferring heat from a low-temperature body to a high-temperature body without external work input
   • Schematic representation of Clausius statement violation
4. 7 Marks
   bWrite down the availability function. Is it a property? Explain it.
   How to answer

   • Define availability function for closed systems: $\phi = u + p_0 v - T_0 s$ or open systems: $\psi = h - T_0 s$
   • Explain that availability function is a property of the composite system consisting of the system and the surroundings/environment at $(T_0, p_0)$
   • Discuss whether it qualifies as a thermodynamic property (point function depending on end states and dead state conditions)
5. 7 Marks
   aWith a neat sketch explain PVT surface of real gas.
   How to answer

   • Draw 3D P-V-T surface showing solid, liquid, vapor/gas regions, two-phase coexistence regions, triple line, and critical point
   • Explain different single-phase and two-phase coexistence regions on the surface
   • Describe projections onto P-v and P-T planes
   • Highlight behavior of substances that contract vs expand upon freezing
6. 7 Marks
   bWith the help of neat sketch explain the working of a separating and throttling calorimeter to find dryness fraction of the steam.
   How to answer

   • Neat schematic diagram of separating and throttling calorimeter
   • Working principle of separating unit (mechanical separation of water droplets, measuring $x_1$)
   • Working principle of throttling unit (superheating steam via throttling, measuring $x_2$ using steam tables)
   • Formula for combined dryness fraction: $x = x_1 \times x_2$
7. 7 Marks
   aDescribe the process of formation of steam and give its graphical representation also.
   How to answer

   • Describe stages of steam formation at constant pressure: subcooled water, saturation temperature, sensible heat
   • Phase change at constant temperature (mixture of water and steam, latent heat of vaporization)
   • Superheating of dry saturated steam
   • Graphical representation on Temperature-Enthalpy ($T-h$) or Temperature-Heat added diagram
8. 7 Marks
   bDetermine the amount of heat, which should be supplied to $2\text{ kg}$ of water at $25^\circ\text{C}$ to convert it into steam at $5\text{ bar}$ and $0.9\text{ dry}$.
   How to answer

   • Initial state: Calculate initial liquid enthalpy $h_1 = c_w T_1 = 4.187 \times 25\text{ kJ/kg} \approx 104.7\text{ kJ/kg}$
   • Final state: Obtain saturation properties at $5\text{ bar}$ from steam tables ($h_f \approx 640.1\text{ kJ/kg}$, $h_{fg} \approx 2108.5\text{ kJ/kg}$)
   • Calculate final enthalpy: $h_2 = h_f + x h_{fg} = 640.1 + 0.9(2108.5) = 2537.75\text{ kJ/kg}$
   • Calculate total heat required: $Q = m(h_2 - h_1) = 2 \times (2537.75 - 104.7) = 4866.1\text{ kJ}$
9. 7 Marks
   aWhat is Carnot cycle? Derive an expression for efficiency of a Carnot cycle.
   How to answer

   • Define Carnot cycle and describe the four reversible processes (isothermal expansion, adiabatic expansion, isothermal compression, adiabatic compression)
   • Draw P-V and T-s diagrams of the cycle
   • Write expressions for heat added $Q_1 = m R T_1 \ln(v_2/v_1)$ and heat rejected $Q_2 = m R T_2 \ln(v_3/v_4)$
   • Derive volume ratio relation: $v_2/v_1 = v_3/v_4$
   • Derive efficiency expression $\eta = 1 - Q_2/Q_1 = 1 - T_2/T_1$
10. 7 Marks
    b$0.3\text{ kg}$ of nitrogen gas at $100\text{ kPa}$ and $40^\circ\text{C}$ is contained in a cylinder. The piston is moved by compressing nitrogen until the pressure becomes $1\text{ MPa}$ and temperature becomes $160^\circ\text{C}$. The work done during the process is $30\text{ kJ}$. Calculate the heat transferred from the nitrogen to the surroundings. $C_v\text{ for nitrogen} = 0.75\text{ kJ/kg K}$.
    How to answer

    • Calculate change in internal energy: $\Delta U = m C_v (T_2 - T_1) = 0.3 \times 0.75 \times (160 - 40) = 27\text{ kJ}$
    • Identify work of compression: $W = -30\text{ kJ}$
    • Apply first law: $Q = \Delta U + W = 27 + (-30) = -3\text{ kJ}$
    • State heat rejected to surroundings is $3\text{ kJ}$
11. 14 Marks
    In an ideal constant volume cycle the pressure and temperature at the beginning of compression are $97\text{ kN/m}^2$ and $40^\circ\text{C}$, respectively. The volume ratio of compression is $7:1$. The heat supplied during the cycle is $1200\text{ kJ/kg}$ of working fluid. Determine: a) the maximum temperature attained in the cycle b) the thermal efficiency of the cycle c) the work done during the cycle/kg of working. Assume $\gamma = 1.4$ and $C_v = 0.718\text{ kJ/kg K}$.
    How to answer

    • Determine $T_1 = 40 + 273.15 = 313.15\text{ K}$
    • Calculate temperature at end of compression: $T_2 = T_1 (r)^{\gamma - 1} = 313.15 \times (7)^{0.4} \approx 682.0\text{ K}$
    • Calculate maximum temperature $T_3$: $T_3 = T_2 + \frac{q_{in}}{C_v} = 682.0 + \frac{1200}{0.718} \approx 2353.3\text{ K}$ ($2080.1^\circ\text{C}$)
    • Calculate thermal efficiency: $\eta_{th} = 1 - \frac{1}{7^{0.4}} \approx 0.5408$ ($54.08\%$)
    • Calculate net work done per kg: $w = \eta_{th} \times q_{in} = 0.5408 \times 1200 \approx 649.0\text{ kJ/kg}$
12. 7 Marks
    aWhat is the significance of enthalpy of formation? How is enthalpy of reaction related to enthalpy of formation?
    How to answer

    • Define enthalpy of formation (heat change when 1 mole of a compound is formed from its constituent elements in standard states)
    • Significance of enthalpy of formation as a baseline thermodynamic property for calculating heats of unknown reactions
    • Relation: $\Delta H_{rxn}^\circ = \sum (n_p \Delta H_{f, products}^\circ) - \sum (n_r \Delta H_{f, reactants}^\circ)$
13. 7 Marks
    bWhat is the difference between actual and theoretical combustion processes?
    How to answer

    • Define theoretical/stoichiometric combustion (exact stoichiometric oxygen required for complete oxidation of all fuel elements, producing only $CO_2$, $H_2O$, $N_2$)
    • Define actual combustion (occurs with excess or deficient air, often incomplete)
    • Key differences: presence of unburned hydrocarbons, $CO$, excess $O_2$, dissociation at high temperatures, soot/smoke formation in actual combustion
14. 14 Marks
    Write short notes on any three of the following: a) Basic concept of third law of thermodynamics b) First law analysis of reacting systems c) Use of steam table and Mollier chart d) Limitations of first law of thermodynamics
    How to answer

    • Third Law: Entropy of a pure crystalline substance approaches zero as absolute temperature approaches zero; concept of absolute entropy
    • Reacting Systems: Energy balance applying First Law taking into account enthalpy of formation and sensible enthalpy: $Q - W = \sum N_p (\bar{h}_f^\circ + \Delta \bar{h})_p - \sum N_r (\bar{h}_f^\circ + \Delta \bar{h})_r$
    • Steam Table & Mollier Chart: Tabular vs graphic ($h-s$ diagram) determination of thermodynamic properties of water/steam, finding enthalpy drop in turbines, throttling lines
    • Limitations of First Law: Does not indicate direction of spontaneous process, feasibility, or extent of conversion of heat into work