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 (9-14%) 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 problem below comes from the PECivilClick FE Mechanical question bank 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 ideal gas law is expressed as:

A) Pv = R/T

B) PV = T

C) Pv = RT

D) P/v = RT

Answer: C) Pv = RT

The ideal gas law relates pressure, specific volume, and temperature:

\(Pv = RT\)

or in terms of total volume:
\(PV = mRT\)

where:
- P = absolute pressure
- v = specific volume (V/m)
- R = specific gas constant
- T = absolute temperature

Problem 2 — A. Properties of ideal gases and pure substances

Air at 300 K and 100 kPa has a density most nearly (R = 0.287 kJ/kg·K):

A) 2.32 kg/m\(^{3}\)

B) 1.50 kg/m\(^{3}\)

C) 0.86 kg/m\(^{3}\)

D) 1.16 kg/m\(^{3}\)

Answer: D) 1.16 kg/m\(^{3}\)

Using ideal gas law:

\(Pv = RT \rightarrow \rho = P/(RT)\)

\(\rho = 100 \text{ kPa} / (0.287 \text{ kJ/kg·K} \times 300 \text{ K})\)

\(\rho = 100 / 86.1 = 1.16 \text{ kg/m}^3\)

Problem 3 — A. Properties of ideal gases and pure substances

The specific gas constant for oxygen (M = 32 kg/kmol) is most nearly:

A) 0.462 kJ/kg·K

B) 0.189 kJ/kg·K

C) 0.260 kJ/kg·K

D) 0.287 kJ/kg·K

Answer: C) 0.260 kJ/kg·K

The specific gas constant:

\(R = \bar{R}/M\)

where \(\bar{R} = 8.314\) kJ/kmol·K (universal gas constant)

\(R = 8.314 / 32 = 0.260\) kJ/kg·K

Problem 4 — A. Properties of ideal gases and pure substances

Steam at 1 MPa has a saturation temperature of 179.9°C. If the actual temperature is 250°C, the steam is:

A) Compressed liquid

B) Superheated

C) Wet (two-phase)

D) Saturated vapor

Answer: B) Superheated

The steam state is determined by comparing actual temperature to saturation temperature:

- \(T_{actual} = 250^{\circ}C\)
- \(T_{sat}\) at 1 MPa \(= 179.9^{\circ}C\)

Since \(T_{actual} > T_{sat}\):

\(\boxed{\text{Superheated vapor}}\)

- If \(T < T_{sat}\) at given P → compressed liquid
- If \(T = T_{sat}\) → saturated
- If \(T > T_{sat}\) → superheated vapor

Problem 5 — A. Properties of ideal gases and pure substances

For an ideal gas, the relationship between specific heats is:

A) cp - cv = R

B) cp \(\times\) cv = R

C) cp / cv = R

D) cp + cv = R

Answer: A) cp - cv = R

For an ideal gas:

\(c_p - c_v = R\)

where:
- \(c_p\) = specific heat at constant pressure
- \(c_v\) = specific heat at constant volume
- R = specific gas constant

Also, \(k = c_p/c_v\) (specific heat ratio).

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

Frequently Asked Questions

How many thermodynamics questions are on the FE Mechanical exam?

NCEES specifies 10-15 questions out of 110, roughly 9-14 percent. 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:

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.