FE Other Disciplines (NCEES Fundamentals of Engineering) — All Questions

The primary purpose of annealing a cold-worked metal is to:

• a.Add carbon to its surface
• b.Soften it and relieve internal stresses by recrystallization✓
• c.Create an extremely hard and brittle martensitic structure throughout
• d.Increase its hardness and strength

Annealing heats the metal enough for recrystallization and grain growth, lowering strength and hardness, restoring ductility, and relieving residual stress left by cold work.

A metal bar with Poisson's ratio 0.30 is stretched to an axial strain of 0.004. What is the magnitude of the resulting transverse (lateral) strain?

• a.0.0004
• b.0.0133
• c.0.0012✓
• d.0.004

Poisson's ratio v = -(lateral strain)/(axial strain), so lateral strain = 0.30 x 0.004 = 0.0012 (a contraction). Most metals have v near 0.3.

For many steels, the 'endurance limit' on an S-N (stress vs. cycles) diagram represents:

• a.The maximum stress reached in a tensile test
• b.A stress below which the material endures essentially infinite cycles✓
• c.The stress at which creep begins
• d.The stress causing fracture in a single load cycle

The endurance (fatigue) limit is a stress amplitude below which steel can sustain effectively unlimited cycles without fatigue failure. Many nonferrous metals lack a true endurance limit.

When zinc and steel are electrically coupled in a moist environment (galvanic corrosion), which metal corrodes preferentially?

• a.Zinc, because it is more anodic (active)✓
• b.Steel, because it is stronger
• c.Neither corrodes
• d.Both corrode equally

The more active (anodic) metal in the galvanic series corrodes and protects the cathode. Zinc is anodic to steel, which is why galvanizing sacrificially protects steel.

A magnesium block bolted to a buried steel pipeline to keep the pipe from rusting is an example of:

• a.Anodizing
• b.Case hardening
• c.Sacrificial-anode cathodic protection✓
• d.Passivation by an oxide film

The magnesium acts as a sacrificial anode, corroding in place of the steel and forcing the pipe to behave as a cathode. This is sacrificial-anode cathodic protection.

Which statement correctly distinguishes a thermoplastic from a thermosetting polymer?

• a.Thermoplastics are permanently cross-linked during curing and therefore, like all thermosets, cannot be remelted or reshaped once formed
• b.Thermoplastics soften on heating and can be remolded, while thermosets are cross-linked and degrade rather than melt✓
• c.Both behave identically when heated
• d.Thermosets can be repeatedly melted and reshaped

Thermoplastics have linear or branched chains that soften and can be reshaped when heated; thermosets form permanent cross-links during curing and cannot be remelted.

Compared with metals, engineering ceramics are generally:

• a.Excellent electrical conductors
• b.Hard and strong in compression but brittle in tension✓
• c.Low in melting temperature
• d.Ductile and strong in tension

Strong ionic and covalent bonds give ceramics high hardness, compressive strength, and melting points, but little plasticity, so they are brittle and weak in tension.

According to the Hall-Petch relationship, decreasing the grain size of a polycrystalline metal will:

• a.Decrease its yield strength
• b.Turn it into a ceramic
• c.Increase its yield strength✓
• d.Have no effect on strength

Grain boundaries impede dislocation motion, so smaller grains (more boundary area) raise yield strength per sigma_y = sigma_0 + k*d^(-1/2).

Cold working (strain hardening) a ductile metal generally:

• a.Increases ductility and toughness while lowering strength and hardness
• b.Lowers both strength and hardness
• c.Increases strength and hardness but reduces ductility✓
• d.Has no effect on mechanical properties

Plastic deformation multiplies and entangles dislocations, raising strength and hardness while reducing ductility. This strain-hardening trade-off is reversed by annealing.

The modulus of resilience of a material is defined as the:

• a.Stress at fracture
• b.Strain energy absorbed per unit volume up to the elastic (yield) limit✓
• c.The total area under the entire engineering stress-strain curve up to fracture
• d.Slope of the elastic region

Resilience is the elastic strain energy stored per unit volume, equal to the area under the stress-strain curve up to yield (about sigma_y^2/2E). The total area to fracture is toughness.

Material toughness, measured by the total area under a stress-strain curve, represents:

• a.The hardness of the surface
• b.Resistance to elastic deflection only
• c.The coefficient of thermal expansion
• d.The total energy absorbed per unit volume before fracture✓

Toughness is the energy per unit volume a material absorbs up to fracture, combining strength and ductility. It differs from stiffness (modulus) and from surface hardness.

Which tensile-test quantity is most commonly used to express a metal's ductility?

• a.Ultimate tensile strength
• b.Young's modulus
• c.Hardness number
• d.Percent elongation at fracture✓

Ductility is typically reported as percent elongation (or percent reduction in area) at fracture, the amount of plastic strain the material sustains before breaking.

A Brinell or Rockwell hardness test primarily measures a material's:

• a.Electrical resistivity
• b.Resistance to localized plastic (indentation) deformation✓
• c.Melting temperature
• d.Fatigue life under repeated fully reversed cyclic loading conditions

Hardness tests press a defined indenter into the surface; hardness is the resistance to localized plastic indentation and correlates roughly with tensile strength in steels.

The linear coefficient of thermal expansion of aluminum is approximately:

• a.0.5 x 10^-6 /degC
• b.23 x 10^-6 /degC✓
• c.200 x 10^-6 /degC
• d.1 x 10^-6 /degC

Aluminum expands about 23 x 10^-6 /degC, roughly twice steel's 12 x 10^-6 /degC. This mismatch drives thermal stresses in bimetallic and composite assemblies.

For an isotropic material with E = 200 GPa and Poisson's ratio 0.30, what is the shear modulus G, where G = E / [2(1 + v)]?

• a.76.9 GPa✓
• b.153.8 GPa
• c.260 GPa
• d.100 GPa

G = E/[2(1 + v)] = 200/[2(1.30)] = 200/2.6 = 76.9 GPa. Only two of E, G, and v are independent for an isotropic elastic solid.

What is the molar mass of calcium carbonate, CaCO3? (Ca = 40, C = 12, O = 16 g/mol)

• a.100 g/mol✓
• b.72 g/mol
• c.116 g/mol
• d.60 g/mol

40 + 12 + 3(16) = 40 + 12 + 48 = 100 g/mol. Summing the atomic masses of every atom in the formula gives the molar (formula) mass.

How many moles are present in 36 g of water (H2O, molar mass 18 g/mol)?

• a.36 mol
• b.2 mol✓
• c.18 mol
• d.0.5 mol

moles = mass / molar mass = 36/18 = 2 mol. The mole links a measurable mass to a number of molecules through Avogadro's number.

What volume does 2 mol of an ideal gas occupy at standard temperature and pressure, where the molar volume is 22.4 L/mol?

• a.44.8 L✓
• b.24.0 L
• c.22.4 L
• d.11.2 L

V = n x 22.4 L/mol = 2 x 22.4 = 44.8 L. At STP one mole of any ideal gas occupies 22.4 L regardless of the gas's identity.

Using PV = nRT, what pressure is exerted by 1 mol of ideal gas in a 24.6 L vessel at 300 K? (R = 0.08206 L·atm/mol·K)

• a.1.0 atm✓
• b.2.0 atm
• c.0.5 atm
• d.24.6 atm

P = nRT/V = (1)(0.08206)(300)/24.6 = 24.6/24.6 = 1.0 atm. The ideal gas law ties P, V, n, and T together through the universal gas constant R.

What is the molarity of a solution containing 0.5 mol of NaCl dissolved in enough water to make 2 L of solution?

• a.0.5 M
• b.2.0 M
• c.0.25 M✓
• d.1.0 M

Molarity = moles of solute / liters of solution = 0.5/2 = 0.25 M. Molarity is defined per liter of total solution, not per liter of solvent.

To what volume must 100 mL of 6.0 M HCl be diluted to obtain a 1.0 M solution? (M1V1 = M2V2)

• a.166 mL
• b.300 mL
• c.60 mL
• d.600 mL✓

V2 = M1V1/M2 = (6.0)(100)/(1.0) = 600 mL. Dilution conserves the moles of solute, so concentration and volume vary inversely.

What is the pH of a 0.01 M solution of the strong base NaOH at 25 degC?

• a.2
• b.7
• c.12✓
• d.10

NaOH dissociates fully, so [OH-] = 0.01, pOH = -log(0.01) = 2, and pH = 14 - pOH = 12. Strong bases give a pH well above 7.

What is the pH of a 1 x 10^-4 M solution of the strong acid HCl?

• a.10
• b.4✓
• c.3
• d.2

HCl dissociates fully, so [H+] = 1 x 10^-4 M and pH = -log(10^-4) = 4. Each tenfold dilution of a strong acid raises the pH by one unit.

In the reaction 2 H2 + O2 -> 2 H2O, how many grams of water form from 2 mol of H2 with excess O2? (H2O = 18 g/mol)

• a.9 g
• b.36 g✓
• c.18 g
• d.72 g

The 2:2 mole ratio gives 2 mol H2 -> 2 mol H2O; mass = 2 x 18 = 36 g. Balanced-equation coefficients set the mole ratios of reactants to products.

For N2 + 3 H2 -> 2 NH3, if 1 mol N2 reacts with 2 mol H2, which is the limiting reactant?

• a.N2
• b.Neither; they are stoichiometric
• c.H2✓
• d.NH3

The reaction needs 3 mol H2 per mol N2, but only 2 mol H2 is available, so hydrogen runs out first and limits the product. Nitrogen is in excess.

What is the mass percent of oxygen in water, H2O? (H = 1, O = 16 g/mol)

• a.88.9%✓
• b.16%
• c.11.1%
• d.50%

Oxygen contributes 16 of the total 18 g/mol, so 16/18 = 88.9%. Mass percent weights each element by its atomic mass, not by atom count.

Approximately how many molecules are in 2 mol of a substance? (Avogadro's number = 6.02 x 10^23 /mol)

• a.3.01 x 10^23
• b.1.20 x 10^23
• c.1.20 x 10^24✓
• d.6.02 x 10^23

Number = n x N_A = 2 x 6.02 x 10^23 = 1.20 x 10^24 molecules. Avogadro's number defines how many entities make up one mole.

What is the oxidation state of manganese in the permanganate ion, MnO4^-? (O = -2)

• a.+2
• b.+7✓
• c.+5
• d.+4

Four oxygens contribute -8; the overall ion charge is -1, so Mn + (-8) = -1, giving Mn = +7. Permanganate is a strong oxidizer because Mn is at its highest state.

When methane burns completely as CH4 + a O2 -> CO2 + b H2O, what are the coefficients a and b?

• a.a = 1, b = 2
• b.a = 2, b = 2✓
• c.a = 2, b = 1
• d.a = 1, b = 1

Balancing carbon gives 1 CO2, hydrogen gives 2 H2O, and oxygen then needs 2 O2: CH4 + 2 O2 -> CO2 + 2 H2O. Every element's atoms must balance.

A first-order reaction has a rate constant k = 0.693 min^-1. What is its half-life? (t-half = 0.693/k)

• a.0.693 min
• b.2.0 min
• c.1.0 min✓
• d.0.5 min

t-half = 0.693/k = 0.693/0.693 = 1.0 min. For first-order kinetics the half-life is constant and independent of the initial concentration.

For the exothermic equilibrium N2 + 3 H2 <=> 2 NH3, increasing the temperature will:

• a.Have no effect on the equilibrium
• b.Shift the equilibrium toward more NH3
• c.Shift the equilibrium toward the reactants (less NH3)✓
• d.Stop the reaction entirely

By Le Chatelier's principle, adding heat to an exothermic reaction favors the endothermic (reverse) direction, decreasing the NH3 yield.

What is the normality of a 2 M sulfuric acid (H2SO4) solution acting as a diprotic acid?

• a.4 N✓
• b.2 N
• c.1 N
• d.0.5 N

Normality = molarity x equivalents per mole. H2SO4 supplies 2 H+ per molecule, so N = 2 x 2 = 4 N. Normality counts reactive equivalents, not just moles.

A water sample contains 5 mg of dissolved solids per liter. Expressed in ppm (mg/L in dilute water), this is:

• a.50 ppm
• b.5 ppm✓
• c.0.5 ppm
• d.500 ppm

In dilute aqueous solution 1 mg/L is about 1 ppm because 1 L of water has a mass near 1 kg (10^6 mg). So 5 mg/L = 5 ppm.

At a fixed temperature and pressure, the density of an ideal gas is directly proportional to its:

• a.Color
• b.Specific heat
• c.Volume
• d.Molar mass✓

From PV = nRT with n = m/M, density rho = PM/(RT). At fixed T and P, density is proportional to molar mass M, so heavier molecules give denser gases.

A reaction releases heat to its surroundings. Its enthalpy change (delta H) is therefore:

• a.Negative (exothermic)✓
• b.Positive (endothermic)
• c.Always equal to the activation energy
• d.Zero

Exothermic reactions release energy, so the products have lower enthalpy than the reactants and delta H < 0. Endothermic reactions absorb heat with delta H > 0.

A compound is 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass (C = 12, H = 1, O = 16). What is its empirical formula?

• a.C2H6O
• b.CH2O✓
• c.C2H4O2
• d.CHO

Moles: C 40/12 = 3.33, H 6.7/1 = 6.7, O 53.3/16 = 3.33. Dividing by 3.33 gives 1:2:1, so CH2O. The empirical formula uses the smallest whole-number atom ratio.

In electrolysis, the mass of metal deposited at the cathode is, by Faraday's laws, proportional to:

• a.The total electric charge (current x time) passed✓
• b.The color of the electrode
• c.The applied voltage only
• d.The temperature of the bath

Faraday's first law states that deposited mass is proportional to the charge Q = I*t passed, scaled by the equivalent weight. Doubling current or time doubles the deposit.

A 4-ohm resistor carries a current of 3 A. What power does it dissipate?

• a.48 W
• b.12 W
• c.1.33 W
• d.36 W✓

Power P = I^2*R = 3^2 x 4 = 9 x 4 = 36 W. The equivalent forms P = VI and P = V^2/R give the same result.

What power is dissipated by a 6-ohm resistor with 12 V across it?

• a.2 W
• b.24 W✓
• c.48 W
• d.72 W

P = V^2/R = 12^2/6 = 144/6 = 24 W. When the voltage is known, P = V^2/R avoids first computing the current.

Three resistors of 2, 3, and 5 ohms are connected in series. What is the total resistance?

• a.3.3 ohms
• b.0.97 ohms
• c.10 ohms✓
• d.1 ohm

Series resistances add directly: 2 + 3 + 5 = 10 ohms. The same current flows through every series element.

A 6-ohm and a 3-ohm resistor are connected in parallel. What is the equivalent resistance?

• a.4.5 ohms
• b.18 ohms
• c.9 ohms
• d.2 ohms✓

R_eq = (R1*R2)/(R1 + R2) = (6 x 3)/(6 + 3) = 18/9 = 2 ohms. A parallel combination is always smaller than the smallest branch.

In a series circuit, 12 V is applied across a 4-ohm and an 8-ohm resistor. What is the voltage across the 8-ohm resistor?

• a.12 V
• b.4 V
• c.6 V
• d.8 V✓

Voltage divider: V8 = 12 x 8/(4 + 8) = 12 x 8/12 = 8 V. Voltage divides in proportion to each series resistance.

Two 4 uF capacitors are connected in series. What is the equivalent capacitance?

• a.0.5 uF
• b.4 uF
• c.8 uF
• d.2 uF✓

Capacitors in series combine like resistors in parallel: 1/C = 1/4 + 1/4, so C = 2 uF. Series capacitance is smaller than either capacitor.

A 2 uF and a 3 uF capacitor are connected in parallel. What is the total capacitance?

• a.1 uF
• b.6 uF
• c.1.2 uF
• d.5 uF✓

Parallel capacitors add directly: 2 + 3 = 5 uF. They share the same voltage, and their stored charges sum.

How much energy is stored in a 100 uF capacitor charged to 10 V? (E = (1/2)CV^2)

• a.0.5 mJ
• b.5 mJ✓
• c.10 mJ
• d.1 mJ

E = (1/2)CV^2 = 0.5 x 100x10^-6 x 10^2 = 0.5 x 100x10^-6 x 100 = 5x10^-3 J = 5 mJ. Capacitors store energy in their electric field.

What charge is stored on a 10 uF capacitor charged to 5 V? (Q = CV)

• a.15 uC
• b.2 uC
• c.0.5 uC
• d.50 uC✓

Q = CV = 10 uF x 5 V = 50 uC. Capacitance is the ratio of stored charge to voltage.

A 1 kohm resistor is in series with a 100 uF capacitor. What is the time constant of the RC circuit?

• a.1 s
• b.0.01 s
• c.0.1 s✓
• d.10 s

tau = RC = 1000 x 100x10^-6 = 0.1 s. After one time constant the capacitor charges to about 63.2% of the supply voltage.

A 2 H inductor is in series with a 4-ohm resistor. What is the time constant of the RL circuit?

• a.0.25 s
• b.2 s
• c.8 s
• d.0.5 s✓

tau = L/R = 2/4 = 0.5 s. A larger inductance or a smaller resistance slows the current's exponential rise.

How much energy is stored in a 2 H inductor carrying 3 A? (E = (1/2)LI^2)

• a.18 J
• b.3 J
• c.9 J✓
• d.6 J

E = (1/2)LI^2 = 0.5 x 2 x 3^2 = 0.5 x 2 x 9 = 9 J. Inductors store energy in their magnetic field.

What is the inductive reactance of a 0.1 H inductor at 60 Hz? (XL = 2*pi*f*L)

• a.0.6 ohms
• b.6 ohms
• c.377 ohms
• d.37.7 ohms✓

XL = 2*pi*f*L = 2*pi*(60)(0.1) = 37.7 ohms. Inductive reactance rises with frequency, so inductors impede high-frequency currents.