Thermodynamics Exam Cheat Sheet: Problem-Solving Recipes

🔹 Problem 1: Property Changes & T-s Sketch

(HW 9 Q1–Q3)
1a. Ideal-Gas Entropy Change

Statement: Air (ideal gas) in a piston-cylinder goes from State 1: T₁ = 350 K, p₁ = 100 kPa to State 2: T₂ = 550 K, p₂ = 700 kPa. Find Δs (kJ/kg·K) (a) reversible, (b) with irreversibilities.

1b. Isothermal Water Compression

Statement: 1 kg water in a piston-cylinder, initially saturated vapor at T = 160 °C, p = 150 kPa, isothermally compressed to saturated liquid. Work on water W = -471.5 kJ. Find (a) Q (kJ), (b) ΔS (kJ/K). Sketch T-s.

Steps for 1a (Ideal Gas)

1. Formula:

   

2. Compute

   • 

3. Evaluate

   

4. Irreversible:

   

Steps for 1b (Water Compression)

1. 1st Law:

   

2. Table Lookup at 160 °C (saturated):

   • 

3. Compute ΔU:

   

4. Compute Q:

   

5. Compute ΔS:

   

6. Sketch T-s:

🔹 Problem 2: Single-Component Device Check

(HW 10 Q1–Q4 & HW 9 Q5–Q10)

Statement: Steady-flow device (turbine or compressor) with inlet (p₁,T₁) and outlet (p₂,T₂_meas). (a) Check feasibility via entropy generation (2nd Law). (b) Use energy balance (1st Law) to find W or Q. (c) Compute isentropic efficiency if asked.

Steps

1. Sketch control volume with inlet 1 and outlet 2.

2. 2nd Law Check:

   

3. Isentropic Efficiency:

   • 

4. 1st Law Steady-Flow:
   

5. Entropy Balance:
   

🔹 Problem 3: Carnot Cycle Analysis

(HW 8 – All Q’s)

Statement: Analyze a Carnot cycle (power, refrigerator, or heat pump) between temperatures T_H and T_C:

• Two isothermals (T_H, T_C)
• Two isentropics

Steps

1. Draw p-v and T-s (or T-v) loops, label states 1→4.

2. List Processes:

   1. Isothermal @ T_H (q_in or q_out)
   2. Adiabatic (isentropic)
   3. Isothermal @ T_C (q_out or q_in)
   4. Adiabatic (isentropic)

3. Compute Each Leg:

   • Isothermal: q=TΔs=h_end-h_start
   • Adiabatic: w=h_start-h_end with s constant.

4. Net Work/Heat: w_net=q_in-q_out.

5. Efficiency/COP:

   η=1-(T_C/T_H), COP_ref=T_C/(T_H-T_C), COP_hp=T_H/(T_H-T_C).

🔹 Problem 4: Integrated Multi-Component Cycle

(HW 10 Q5–Q9 & HW 7 Q4–Q5)

Statement: Full Rankine or combined-cycle plant: boiler → turbine(s) → condenser → pump(s) → reheater/heat exchanger. Find net power, η_th, component η’s, cooling-water flow, entropy generation.

Steps

1. Sketch full plant, label all states.

2. State Table: p, T, h, s, x.

3. Turbine/Nozzle:

   w_t=h_in-h_out,act, η_t=(h_in-h_out,act)/(h_in-h_out,s)

4. Pump/Compressor:

   w_p=h_out,act-h_in, η_p=(h_out,s-h_in)/(h_out,act-h_in)
   with w_p,s ≈ v(P_out-P_in).

5. Heat Duties:
   q_in=h_boiler,out-h_boiler,in, q_out=h_cond,in-h_cond,out

6. Net Work & Efficiency:
   w_net=∑w_t-∑w_p, η_th=w_net/q_in

7. Cooling-Water Flow:
   ṁ_w=Q_out/(c_p,w(T_w,out-T_w,in))

8. Entropy-Generation:
   Ṡ_gen=∑ṁ(s_out-s_in)+∑(Q/T_b)≥0

Use this sheet verbatim. Each problem includes its statement, source, and a numbered recipe—only algebra and table lookups remain. Good luck!