Thermodynamics is 10-15 questions on the FE Mechanical exam, tied for the largest area and the one that most distinguishes this exam from FE Civil, where it does not appear at all.
Nearly every question here begins with the same two decisions: what is the system, and is the process closed or open. Candidates who make those decisions explicitly on paper move quickly; candidates who start substituting into equations do not.
Exam weight: NCEES lists Thermodynamics at 10-15 questions of the 110-question FE Mechanical exam. Work each problem below on paper first, then reveal the worked solution — reading a solution you have not attempted builds recognition, not recall.
What NCEES Tests in Thermodynamics
The specification covers properties of ideal gases and pure substances, energy transfers, the laws of thermodynamics, processes, performance of components, power cycles, refrigeration and heat pump cycles, and mixtures of non-reactive gases. Expect a steam table interpolation, a first-law energy balance on a turbine or compressor, an isentropic efficiency, and a cycle thermal efficiency or coefficient of performance.
Second-law items ask for entropy change or test whether a proposed device is possible. A Carnot efficiency computed from reservoir temperatures is the standard check, and it must be done in absolute temperature.
5 Free Thermodynamics Practice Problems
Each thermodynamics problem below comes from the FEExamClick FE Mechanical question bank, with worked solutions, and matches the style, difficulty and format of the real exam. Attempt each one under a three-minute limit — roughly the pace the exam demands.
Problem 1 — A. Properties of ideal gases and pure substances
The pressure (kPa) of 100 kg of nitrogen (N\(_{2}\)) at 70°C in a 100-m\(^{3}\) tank is most nearly:
Answer: C) 102
Refer to the Properties of Single-Component Systems section in the Thermodynamics chapter of the FE Reference Handbook.
For an ideal gas: PV = mRT
$$R for N_2 = \bar{R}/M = 8.314/28 = 0.2969 kJ/(kg\cdot K)$$
$$T = 70 + 273 = 343 K$$
$$\boxed{P = mRT/V = (100)(0.2969)(343)/100 = 101.8 kPa \approx 102 kPa}$$
Problem 2 — B. Energy transfers
A gas in a piston-cylinder assembly undergoes a polytropic process (PV^1.3 = constant) from 150 kPa, 0.05 m\(^{3}\) to 700 kPa, 0.015 m\(^{3}\). The boundary work (kJ) is most nearly:
Answer: B) −10.0
Refer to the Closed-System (Boundary) Work entry in the First Law section of the Thermodynamics chapter of the FE Reference Handbook.
Polytropic boundary work (\(PV^n\) = constant, \(n \ne 1\)) is the area under the curve on the P–V plane, and it reduces to the end-state \(PV\) products:
\(W = \dfrac{P_2 V_2 - P_1 V_1}{1 - n}\)
Note the volume ratio has already been fixed by the two given states, so no property tables are needed — only the end-point \(PV\) products and the exponent \(n\).
End-state products (recall \(1\ \text{kPa}\cdot\text{m}^3 = 1\ \text{kJ}\)):
\(P_1 V_1 = (150)(0.05) = 7.5\ \text{kJ}, \qquad P_2 V_2 = (700)(0.015) = 10.5\ \text{kJ}\)
$$W = \dfrac{10.5 - 7.5}{1 - 1.3} = \dfrac{3.0}{-0.3} = -10.0\ \text{kJ}$$
The negative sign is expected: the gas is compressed (V drops from 0.05 to 0.015 m³), so the surroundings do work on the gas.
Why the other options fail:
• +10.0 kJ — correct magnitude, wrong sign (numerator reversed). Compression can never give positive boundary work.
• −7.5 kJ — used the air value \(n = 1.4\) instead of the stated \(n = 1.3\): \(3.0/(1-1.4) = -7.5\).
• −3.0 kJ — forgot the \(1/(1-n)\) factor and reported just \(P_2V_2 - P_1V_1\).
Correct answer: (B) −10.0 kJ
Problem 3 — H. Nonreacting mixtures of gases
A mixture of ideal gases at 500 kPa consists of 40% N\(_{2}\), 35% O\(_{2}\), and 25% CO\(_{2}\) by mole. The partial pressure of O\(_{2}\) (kPa) is most nearly:
Answer: B) 175
Refer to the Ideal Gas Mixtures section in the Thermodynamics chapter of the FE Reference Handbook.
Partial pressure: \(P_i = y_i \times P_{total}\)
$$\boxed{P_{O_2} = 0.35 \times 500 = 175 kPa}$$
Problem 4 — C. Laws of thermodynamics
A heat engine receives 500 kJ of heat from a source at 600 K and rejects 300 kJ to a sink at 300 K. The entropy generation (kJ/K) for this cycle is most nearly:
Answer: A) 0.167
Refer to the Second Law of Thermodynamics section (p. 150) in the Thermodynamics chapter of the FE Reference Handbook.
$$For a cyclic device, \Delta S_{system} = 0.$$
Entropy generation:
\(S_{gen} = -Q_H/T_H + Q_L/T_L\)
$$S_{gen} = -500/600 + 300/300 = -0.833 + 1.000 = 0.167 kJ/K$$
Since \(S_{\text{gen}}\) > 0, the cycle is irreversible (satisfies the second law).
Problem 5 — J. Heating, ventilation, and air-conditioning (HVAC) processes
Outdoor air at 40°C and 30% RH is mixed with return air at 24°C and 50% RH. The outdoor air fraction is 20%. Using cp = 1.005 kJ/(kg·K), the mixed air dry-bulb temperature (°C) is most nearly:
Answer: C) 27.2
Refer to the Adiabatic Mixing section (p. 459) in the Mechanical Engineering chapter of the FE Reference Handbook.
For adiabatic mixing of air streams (sensible temperature):
$$T_{mix} = f_1 \times T_1 + f_2 \times T_2$$
$$where f_1 = outdoor fraction = 0.20, f_2 = return fraction = 0.80$$
$$\boxed{T_{mix} = 0.20 \times 40 + 0.80 \times 24 = 8.0 + 19.2 = 27.2^{\circ}C}$$
Using the FE Reference Handbook for Thermodynamics
The property tables are the centre of this section and the reason candidates run out of time. Practise the saturated-mixture workflow until it is automatic: find the pressure or temperature row, read the saturated liquid and vapour values, then interpolate with quality. Also fix in your memory that the tables are ordered separately for temperature-entry and pressure-entry, because opening the wrong one costs a minute each time.
Four Mistakes That Cost Points
- Working in Celsius where Kelvin is required. Any ratio of temperatures, including Carnot efficiency and isentropic relations, needs absolute temperature. Only a temperature difference may be taken in Celsius. This is the most common single error in the area.
- Applying a closed-system energy balance to a flow device. A turbine, pump, compressor or nozzle is an open system, so enthalpy carries the flow work. Using internal energy for these devices produces a wrong answer that is always among the options.
- Ignoring quality in the two-phase region. Inside the vapour dome, pressure and temperature are not independent, so a property must be found by interpolating between saturated liquid and saturated vapour values with quality. Reading a superheated table instead gives a plausible but wrong number.
- Confusing isentropic efficiency's numerator and denominator. For a turbine, efficiency is actual work over isentropic work; for a compressor or pump it is the reverse. Inverting the ratio gives a value above one, and if you do not notice that, the reciprocal is on the answer list.
Frequently Asked Questions
How many thermodynamics questions are on the FE Mechanical exam?
NCEES specifies 10-15 questions out of 110. It is tied with Dynamics, Fluid Mechanics and Mechanical Design and Analysis for the largest knowledge area on the exam.
How much steam table work should I expect?
Enough that speed matters. Several questions per exam require reading or interpolating a property table, and each one that takes three minutes instead of one costs you elsewhere. Drill the saturated-mixture and superheated lookups until the sequence is automatic.
Which cycles are tested?
Rankine, Brayton, Otto, Diesel and the vapour-compression refrigeration cycle all appear. You are more often asked for thermal efficiency, back-work ratio or coefficient of performance than for a full state-by-state analysis, so know what defines each cycle and which processes it contains.
Does thermodynamics appear on the FE Civil exam?
No. It is one of the areas unique to FE Mechanical, together with Heat Transfer, Measurements and Controls, and Mechanical Design and Analysis. Together those four are worth roughly a third of the FE Mechanical paper.
Keep Going
These topics feed into each other on the exam:
- FE Mechanical Heat Transfer practice problems — 7-11 questions on the exam
- FE Mechanical Fluid Mechanics practice problems — 10-15 questions on the exam
- FE Mechanical Mechanical Design and Analysis practice problems — 10-15 questions on the exam
Done with thermodynamics? Browse every knowledge area from the free FE Mechanical practice problem hub, see what the full bank covers on the FE Mechanical exam prep page, or plan your schedule with the FE study timeline. Or test yourself against the clock with the free FE Mechanical practice exam: 20 timed questions in the CBT format.