ME-302 Thermodynamics - Jun 2023 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
   aState the first law of thermodynamics and prove for a non flow process it leads to the energy equation $Q = dU + W$.
   How to answer

   • State First Law of Thermodynamics for a cycle: cyclic integral of heat equals cyclic integral of work
   • Apply the law to a system executing a cycle comprising two processes
   • Show that $(dQ - dW)$ is a property of the system, defined as internal energy $dU$
   • Conclude with the non-flow energy equation $Q = dU + W$ (or $\delta Q = dU + \delta W$)
2. 7 Marks
   bThe properties of a closed system change following the relationship between pressure and volume as $pv = 3.0$, where $p$ is the pressure and $v$ is the volume in $\text{m}^3$ calculate the work done when the pressure increases from $1.5\text{ bar}$ to $7.5\text{ bar}$.
   How to answer

   • Identify process: $pv = C = 3.0$
   • Express work integral: $W = \int_{v_1}^{v_2} p dv = C \ln(p_1/p_2)$
   • Convert pressure units if necessary (or note $pv$ is given as constant)
   • Substitute values: $W = 3.0 \times 10^5 \ln(1.5 / 7.5)$ or compute in appropriate consistent units
   • Calculate final numerical value of work done (negative sign indicating work done on system)
3. 7 Marks
   aDefine enthalpy of a system and internal energy.
   How to answer

   • Define Internal Energy ($U$) as the microscopic energy of the molecular structure and activity
   • Define Enthalpy ($H$) as total heat content given by $H = U + pV$
   • State units and point out both are extensive state properties
4. 7 Marks
   bA cylinder contain $4.5\text{ m}^3$ of gas at $10^5\text{ N/m}^2$ and $80^\circ\text{C}$. The gas is compressed to a volume of $0.13\text{ m}^3$, The final pressure being $5 \times 10^5\text{ N/m}^2$. Determine: i) the mass of the gas ii) The value of index 'n' of compression iii) heat received or rejected by the gas during compressor take $\gamma = 1.4$ and $R = 294.2\text{ j/kg}^\circ\text{C}$
   How to answer

   • Convert $T_1 = 80 + 273.15 = 353.15\text{ K}$
   • Calculate mass using ideal gas equation: $m = \frac{p_1 V_1}{R T_1}$
   • Determine index $n$ using $p_1 V_1^n = p_2 V_2^n \implies n = \frac{\ln(p_2/p_1)}{\ln(V_1/V_2)}$
   • Compute polytropic work $W = \frac{p_1 V_1 - p_2 V_2}{n - 1}$
   • Calculate heat transfer $Q = \left(\frac{\gamma - n}{\gamma - 1}\right) W$ and state if heat is rejected
5. 7 Marks
   aA reversible heat engine operates between two reservoirs temperatures of $700^\circ\text{C}$ and $50^\circ\text{C}$. The engine drives a reversible Refrigerator which operates between reservoirs at temperature of $50^\circ\text{C}$ and $-25^\circ\text{C}$ the heat transfer to the engine is $2500\text{ kJ}$ and the network output of the combined engine and refrigerator plant is $400\text{ kJ}$. Determine the heat transfer to the refrigerant and net heat transfer to the reservoir at $50^\circ\text{C}$.
   How to answer

   • Convert temperatures to Kelvin: $T_1 = 973.15\text{ K}$, $T_2 = 323.15\text{ K}$, $T_3 = 248.15\text{ K}$
   • Calculate Carnot engine efficiency $\eta_E = 1 - T_2/T_1$ and work output $W_E = \eta_E Q_1$
   • Determine work input to refrigerator: $W_R = W_E - W_{net}$
   • Calculate COP of reversible refrigerator: $\text{COP} = T_3 / (T_2 - T_3)$
   • Find heat absorbed by refrigerator $Q_4 = \text{COP} \times W_R$
   • Calculate heat rejected to $50^\circ\text{C}$ reservoir: $Q_{2} = Q_1 - W_E$ and $Q_{rej, R} = Q_4 + W_R$, then find net heat to $50^\circ\text{C}$
6. 7 Marks
   bState the Clausius statement of second law of thermodynamics.
   How to answer

   • State Clausius statement verbatim: It is impossible for any system to operate in such a manner that the sole result would be an energy transfer by heat from a cooler to a hotter body without external work input
   • Brief physical interpretation regarding refrigerators and heat pumps
7. 7 Marks
   aWhat is triple point explain with neat diagram and also explain the p-V-T surface.
   How to answer

   • Define triple point: the thermodynamic state where solid, liquid, and vapor phases coexist in equilibrium
   • Draw p-T phase diagram showing the triple point line/point
   • Explain p-V-T surface with neat 3D sketch showing single-phase regions and two-phase coexistence regions
8. 7 Marks
   bExplain the following terms in relation with the steam formation. i) Sensible heat and latent heat of water ii) Enthalpy of wet steam and superheated steam
   How to answer

   • Define sensible heat: heat required to raise temperature of water to boiling point ($h_f$)
   • Define latent heat: heat required to convert saturated liquid to saturated vapor at constant pressure ($h_{fg}$)
   • Write formula for wet steam enthalpy: $h = h_f + x h_{fg}$
   • Write formula for superheated steam enthalpy: $h_{sup} = h_g + c_{p,steam}(T_{sup} - T_{sat})$
9. 7 Marks
   aSteam enters an Engine at a pressure $10\text{ bar}$ absolute and $400^\circ\text{C}$. It is exhausted at $0.2\text{ bar}$. The steam at exhaust is $0.9\text{ dry}$. Find: i) Drop in Enthalpy ii) Change in entropy
   How to answer

   • Obtain properties from steam tables for superheated steam at $10\text{ bar}$ and $400^\circ\text{C}$ to find $h_1$ and $s_1$
   • Obtain saturation properties at $0.2\text{ bar}$ ($h_f, h_{fg}, s_f, s_{fg}$)
   • Calculate $h_2 = h_f + x_2 h_{fg}$ and $s_2 = s_f + x_2 s_{fg}$ with $x_2 = 0.9$
   • Calculate drop in enthalpy $\Delta h = h_1 - h_2$
   • Calculate change in entropy $\Delta s = s_2 - s_1$
10. 7 Marks
    bDoes wet steam obey laws of perfect gases. Discuss.
    How to answer

    • State clearly that wet steam does NOT obey the ideal/perfect gas laws ($pv = RT$)
    • Explain that wet steam is a two-phase mixture of liquid droplets and vapor
    • Discuss phase change effects: pressure and temperature are dependent on each other
    • Mention that only highly superheated steam at low pressures approximates perfect gas behavior
11. 7 Marks
    aWhat is cycle ? What is the difference between an ideal cycle and actual cycle?
    How to answer

    • Define a thermodynamic cycle: a sequence of processes that begins and ends at the same state
    • Compare ideal vs actual cycles on parameters: reversibility (reversible vs irreversible)
    • Account for real phenomena: friction, heat losses, incomplete combustion, variable specific heats
    • Note difference in theoretical vs brake/indicated thermal efficiency
12. 7 Marks
    bDerive the expression of Air standard efficiency of Diesel cycle.
    How to answer

    • Sketch p-V and T-s diagrams of Diesel cycle showing all 4 processes
    • Express heat addition: $Q_{in} = m c_p (T_3 - T_2)$ and heat rejection: $Q_{out} = m c_v (T_4 - T_1)$
    • Write basic efficiency formula $\eta = 1 - \frac{Q_{out}}{Q_{in}} = 1 - \frac{T_4 - T_1}{\gamma(T_3 - T_2)}$
    • Define compression ratio $r = V_1/V_2$ and cut-off ratio $r_c = V_3/V_2$
    • Express temperatures in terms of $r$, $r_c$, and $T_1$ to derive: $\eta_{diesel} = 1 - \frac{1}{r^{\gamma-1}} \left[ \frac{r_c^\gamma - 1}{\gamma(r_c - 1)} \right]$
13. 7 Marks
    aWhat are primary fuels ? List out some primary fuels and define heating value of fuel.
    How to answer

    • Define primary fuels as natural fuels that are used directly without chemical alteration
    • List examples: coal, wood, crude petroleum, natural gas
    • Define heating value (calorific value) as the amount of heat released per unit mass/volume during complete combustion
    • Briefly distinguish between Higher Heating Value (HHV) and Lower Heating Value (LHV)
14. 7 Marks
    bA steam boiler uses pulverized coal in the furnace. The ultimate analysis of coal as reserved (by weight) is $\text{C} = 78\%$; $\text{H}_2 = 3\%$; ash is $10\%$ and moisture is $5\%$, Excess air supplied is $30\%$, calculate the weight of air supplied and weight of gaseous product formed per kg of coal burnt.
    How to answer

    • Determine oxygen needed for combustion: $O_2 = \frac{8}{3}C + 8H_2 = \frac{8}{3}(0.78) + 8(0.03)$
    • Calculate stoichiometric air required: $\text{Air}_{th} = \frac{O_2}{0.23}$
    • Calculate actual air supplied with $30\%$ excess: $\text{Air}_{actual} = 1.30 \times \text{Air}_{th}$
    • Determine individual products of combustion: $\text{CO}_2$, $\text{H}_2\text{O}$ (from hydrogen and moisture), $\text{O}_2$ (excess), and $\text{N}_2$
    • Sum the gaseous constituents (or apply mass balance: $\text{Gas weight} = 1 - \text{ash} + \text{Air}_{actual}$) to obtain the weight of gaseous products per kg of coal
15. 14 Marks
    Write a short note on any two: a) Boyle's law and Charle's law b) Kelvin Plank statement of second law of thermodynamics c) Actual and theoretical combustion process d) Brayton cycle
    How to answer

    • For (a): State Boyle's Law ($p \propto 1/V$ at constant $T$) and Charles's Law ($V \propto T$ at constant $p$)
    • For (b): State Kelvin-Planck statement (impossible to construct a heat engine operating in a cycle whose sole effect is extracting heat from a single reservoir and producing net work)
    • For (c): Contrast theoretical (stoichiometric) combustion with actual combustion (requiring excess air, presence of incomplete combustion products like CO)
    • For (d): Explain Brayton cycle as ideal gas turbine cycle; draw p-v and T-s diagrams; list component processes (compression, constant-p heat addition, expansion, constant-p heat rejection)