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PE Mechanical HVAC practice questions

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Question 1Basic Engineering Practice

A fan motor is rated at 1 Btu/h of heat-equivalent output. What is this rate expressed in watts?

  1. 0.293 W Correct answer.
  2. 1055 W
  3. 3.412 W
  4. 1.055 W

Explanation

One Btu equals approximately 1,055 J, so a rate of 1 Btu/h is 1,055 J divided by 3,600 s, or about 0.293 W. The conversion factor between Btu/h and watts is therefore 1 Btu/h = 0.293 W.

Question 2Basic Engineering Practice

How many significant figures are in the measured value 0.004560 m?

  1. 3
  2. 4 Correct answer.
  3. 7
  4. 5

Explanation

Leading zeros that merely locate the decimal point are not significant, while zeros to the right of the last nonzero digit in a decimal number are significant. Counting from the 4 gives 4, 5, 6, and the trailing 0, for four significant figures.

Question 3Basic Engineering Practice

A $10,000 loan carries simple interest at 6% per year for 3 years. What total amount is repaid at the end of the term?

  1. $11,200
  2. $11,800 Correct answer.
  3. $12,100
  4. $11,910

Explanation

Simple interest accrues only on the original principal: I = P x i x n = $10,000 x 0.06 x 3 = $1,800. The repayment is therefore $10,000 + $1,800 = $11,800.

Question 4Basic Engineering Practice

A licensed HVAC engineer is asked to seal mechanical drawings for a plumbing system prepared by an unlicensed colleague in another discipline. Under the NCEES Model Rules, the engineer should:

  1. Seal the drawings if the client accepts the risk in writing
  2. Seal the drawings once the colleague signs a written waiver
  3. Decline and refer the work to an engineer competent in that discipline Correct answer.
  4. Seal the drawings because a professional seal covers all disciplines

Explanation

Engineers may seal only work they prepared or that was prepared under their responsible charge, and only within their areas of competence. A seal is not a general endorsement of work performed by others or outside the engineer's field.

Question 5Basic Engineering Practice

A technician will replace the belt on a rooftop supply fan driven by a remote variable-frequency drive. What is the minimum acceptable safety practice before work begins?

  1. Notify the building owner and then proceed with the work
  2. Open the local disconnect and begin work immediately
  3. Command the drive to stop from the building automation system
  4. Isolate the circuit, apply a lock and tag, and verify the absence of voltage Correct answer.

Explanation

Servicing requires a full lockout/tagout: the energy source must be isolated, locked and tagged by the person doing the work, and the absence of voltage verified at the equipment. Control commands and unverified open disconnects do not protect against remote restart or stored energy.

Question 6Basic Engineering Practice

In a critical path method (CPM) schedule, the critical path is the sequence of activities that:

  1. Has the shortest total duration from start to finish
  2. Contains the greatest number of parallel branches
  3. Has the longest total duration from start to finish Correct answer.
  4. Contains the greatest number of activities

Explanation

The critical path is the longest-duration path through the network, so it sets the shortest possible project completion time. Activities on it have zero total float, and any delay on the path delays the whole project.

Question 7Basic Engineering Practice

One ton of refrigeration is equivalent to which cooling rate?

  1. 200 Btu/h
  2. 12,000 Btu/h Correct answer.
  3. 1,055 Btu/h
  4. 3,517 Btu/h

Explanation

One ton of refrigeration is defined as the rate of heat removal needed to freeze one short ton of ice per day, which is 12,000 Btu/h. The same capacity equals about 3.517 kW.

Question 8Basic Engineering Practice

A pressure gauge on a chilled-water loop reads 100 psig at a location where atmospheric pressure is 14.7 psi. What is the absolute pressure?

  1. 85.3 psia
  2. 114.7 psia Correct answer.
  3. 14.7 psia
  4. 100 psia

Explanation

Gauge pressure is measured relative to the local atmosphere, so absolute pressure equals gauge pressure plus atmospheric pressure. Adding 100 psig and 14.7 psi gives 114.7 psia.

Question 9Basic Engineering Practice

A deposit of $5,000 earns 8% per year compounded annually. What is the balance after 10 years?

  1. $12,950
  2. $10,795
  3. $5,400
  4. $9,000 Correct answer.

Explanation

Compound interest grows the balance by the single-payment factor (1 + i)^n, so F = $5,000(1.08)^10 = $5,000(2.1589) = $10,795. Compounding causes the balance to exceed a simple-interest result.

Question 10Basic Engineering Practice

What is the present worth of a uniform series of $1,200 per year for 8 years at an interest rate of 7% per year?

  1. $8,400
  2. $7,166 Correct answer.
  3. $9,600
  4. $6,844

Explanation

The present worth of a uniform series uses the factor (P/A, 7%, 8) = [(1.07)^8 - 1]/[0.07(1.07)^8] = 5.971. Multiplying by $1,200 gives about $7,166.

Question 11Basic Engineering Practice

A $50,000 loan is repaid in 15 equal annual payments at 6% per year. What is the annual payment?

  1. $5,148 Correct answer.
  2. $3,000
  3. $3,333
  4. $6,667

Explanation

The payment is found with the capital recovery factor (A/P, 6%, 15) = 0.06(1.06)^15/[(1.06)^15 - 1] = 0.10296. Applying it to $50,000 gives about $5,148 per year.

Question 12Basic Engineering Practice

A project is evaluated using a market interest rate of 9% per year when general inflation is running at 3.5% per year. What is the real (inflation-free) rate of return?

  1. 5.31% Correct answer.
  2. 6.00%
  3. 12.50%
  4. 5.50%

Explanation

The real rate is obtained from (1 + i) = (1 + i_real)(1 + f), so i_real = 1.09/1.035 - 1 = 5.31%. Simple subtraction of inflation from the market rate is only an approximation.

Question 13Basic Engineering Practice

A chiller with an installed cost of $80,000 has a salvage value of $5,000 and a 10-year depreciable life under straight-line depreciation. What is its book value after 3 years?

  1. $57,500 Correct answer.
  2. $42,500
  3. $72,500
  4. $65,000

Explanation

Straight-line depreciation is ($80,000 - $5,000)/10 = $7,500 per year. After 3 years the accumulated depreciation is $22,500, leaving a book value of $80,000 - $22,500 = $57,500.

Question 14Basic Engineering Practice

A retrofit yields annual revenue of $100,000, annual operating cost of $40,000, and depreciation of $20,000. With an effective tax rate of 25%, what is the after-tax cash flow each year?

  1. $45,000
  2. $60,000
  3. $40,000
  4. $50,000 Correct answer.

Explanation

Taxable income is $100,000 - $40,000 - $20,000 = $40,000, so tax is $10,000 and net income is $30,000. Adding back the non-cash depreciation gives an after-tax cash flow of $30,000 + $20,000 = $50,000.

Question 15Basic Engineering Practice

A product sells for $45 per unit with a variable cost of $25 per unit. If fixed costs are $120,000 per year, what annual sales volume breaks even?

  1. 7,500 units
  2. 6,000 units Correct answer.
  3. 4,800 units
  4. 2,667 units

Explanation

The contribution margin per unit is $45 - $25 = $20, and break-even volume is fixed cost divided by contribution margin. Thus $120,000/$20 = 6,000 units per year.

Question 16Basic Engineering Practice

A project has present worth of benefits of $900,000 and present worth of costs of $600,000. What is the benefit-cost ratio?

  1. 0.67
  2. 1.20
  3. 1.50 Correct answer.
  4. 2.50

Explanation

The benefit-cost ratio is the present worth of benefits divided by the present worth of costs, or $900,000/$600,000 = 1.50. A ratio greater than 1.0 indicates that benefits exceed costs.

Question 17Basic Engineering Practice

A project has earned value of $400,000, actual cost of $500,000, and planned value of $450,000. What is the cost performance index?

  1. 0.89
  2. 1.25
  3. 0.80 Correct answer.
  4. 1.13

Explanation

The cost performance index is earned value divided by actual cost, or $400,000/$500,000 = 0.80. A CPI below 1.0 means the work performed is costing more than was budgeted.

Question 18Basic Engineering Practice

Water with density 1,000 kg/m3 and viscosity 0.001 Pa-s flows at 2 m/s through a pipe of 0.05 m inside diameter. What is the Reynolds number?

  1. 100,000 Correct answer.
  2. 2,500
  3. 1,000,000
  4. 10,000

Explanation

Reynolds number is Re = (rho)(V)(D)/mu = (1,000)(2)(0.05)/0.001 = 100,000. This is well above the usual transition value near 2,300, so the flow is fully turbulent.

Question 19Basic Engineering Practice

Five repeated measurements of a duct velocity are 2, 4, 4, 4, and 6 m/s. What is the sample standard deviation?

  1. 1.26 m/s
  2. 2.00 m/s
  3. 1.41 m/s Correct answer.
  4. 1.79 m/s

Explanation

The mean is 4 m/s and the sum of squared deviations is 4 + 0 + 0 + 0 + 4 = 8. The sample standard deviation divides by n - 1 = 4, giving s = sqrt(8/4) = 1.41 m/s.

Question 20Basic Engineering Practice

A measured quantity is normally distributed with a mean of 100 and a standard deviation of 10. Approximately what percentage of readings exceed 120?

  1. 0.62%
  2. 2.28% Correct answer.
  3. 15.87%
  4. 4.55%

Explanation

A value of 120 lies two standard deviations above the mean, so z = 2. The one-sided area beyond z = 2 is about 0.0228, or 2.28% of readings.

Question 21Basic Engineering Practice

A 200 gpm pump package costs $50,000. Using the six-tenths rule with no other adjustments, what is the estimated cost of a 400 gpm package of similar design?

  1. $85,000
  2. $75,800 Correct answer.
  3. $65,800
  4. $100,000

Explanation

The six-tenths rule estimates cost by capacity ratio raised to the 0.6 power: $50,000 x (400/200)^0.6 = $50,000 x 1.516 = $75,800. Capacity scaling is sublinear, so doubling capacity less than doubles cost.

Question 22Basic Engineering Practice

A cooling tower was budgeted at $250,000 when the cost index stood at 400. The current index for the same equipment type is 520. What is the escalated cost estimate?

  1. $325,000 Correct answer.
  2. $312,500
  3. $192,300
  4. $400,000

Explanation

Cost index escalation multiplies the historical cost by the ratio of the new index to the old index: $250,000 x (520/400) = $325,000. The index rose 30%, so the estimate rises by the same proportion.

Question 23Basic Engineering Practice

A $10,000 investment produces uniform annual savings of $2,500 for 6 years with no salvage value. What is the internal rate of return?

  1. 9%
  2. 13% Correct answer.
  3. 11%
  4. 16%

Explanation

The internal rate of return makes the present worth of the savings equal the first cost, so (P/A, i, 6) must equal $10,000/$2,500 = 4.00. Interpolating between 12% (4.111) and 13% (3.998) places the rate at about 13%.

Question 24Basic Engineering Practice

Two chiller options are compared at 8% per year. Option A costs $40,000, lasts 5 years, and has $5,000/yr maintenance. Option B costs $60,000, lasts 10 years, and has $3,000/yr maintenance. Both have zero salvage value. What is the equivalent annual cost of the more economical option?

  1. $13,500
  2. $15,020
  3. $11,940 Correct answer.
  4. $8,940

Explanation

Equivalent annual cost converts each first cost to a level annual charge with the capital recovery factor and adds maintenance. Option B gives $60,000(0.14903) + $3,000 = $11,940, which is lower than Option A's $15,020, so Option B is preferred.

Question 25Basic Engineering Practice

A maintenance contract costs $10,000 in the first year and escalates 5% per year for 10 years. What is the present worth at an 8% per year discount rate?

  1. $72,500
  2. $81,800 Correct answer.
  3. $100,000
  4. $67,100

Explanation

An escalating series is discounted with the geometric gradient factor [1 - ((1+g)/(1+i))^n]/(i - g). Here that factor is [1 - (1.05/1.08)^10]/0.03 = 8.183, giving a present worth of about $81,800.

Question 26Basic Engineering Practice

A supply fan is rated to deliver 400 cfm of air. Using 1 cfm = 0.4719 L/s, what is the equivalent volumetric flow rate?

  1. 679 L/s
  2. 188.8 L/s Correct answer.
  3. 0.189 L/s
  4. 8.5 L/s

Explanation

Volumetric flow converts by multiplying the cfm value by the factor 0.4719 L/s per cfm, giving 400 × 0.4719 = 188.8 L/s. Equivalently, 1 cfm equals about 0.0004719 m3/s, so the conversion must move the decimal three places when expressing the result in liters.

Question 27Basic Engineering Practice

An engineer reviewing a project discovers that a calculation error in a colleague's design has already been released for construction. According to standard engineering ethics practice, the most appropriate first action is to:

  1. Defer the concern to the next scheduled project review
  2. Notify the responsible engineer and the supervisor in writing Correct answer.
  3. Inform the client directly and let the client order the fix
  4. Quietly revise the drawings and issue a corrected set

Explanation

Ethical practice requires that known errors affecting public safety or project quality be raised promptly through established lines of authority so the responsible party can evaluate and correct them, and so the notification is documented. Bypassing the responsible engineer or the client's chain of command disrupts accountability, while silence or delay leaves a known defect in place.

Question 28Basic Engineering Practice

A duct airflow is computed as velocity times area. The velocity measurement carries a relative uncertainty of ±3% and the duct area carries a relative uncertainty of ±2%, with the errors independent and random. What is the relative uncertainty of the computed flow rate?

  1. ±1.0%
  2. ±3.6% Correct answer.
  3. ±2.5%
  4. ±5.0%

Explanation

For a product of independently measured quantities, relative uncertainties combine in quadrature: u_Q/Q = sqrt[(u_V/V)^2 + (u_A/A)^2] = sqrt(0.03^2 + 0.02^2) = 0.036, or ±3.6%. Adding the percentages arithmetically overstates the uncertainty because the two random errors are unlikely to peak simultaneously.

Question 29Basic Engineering Practice

Four independent dimensions are stacked in series, and each carries an equal-bilateral tolerance of ±0.004 in. Using the statistical (root-sum-square) method rather than worst case, the tolerance on the overall stack length is:

  1. ±0.002 in
  2. ±0.016 in
  3. ±0.008 in Correct answer.
  4. ±0.004 in

Explanation

The root-sum-square method combines independent tolerances as t_stack = sqrt(t1^2 + t2^2 + t3^2 + t4^2) = sqrt(4 × 0.004^2) = 0.004 × 2 = ±0.008 in. This reflects the low probability that all four dimensions simultaneously reach their extremes, and it yields a tighter assembly tolerance than simple addition.

Question 30Thermodynamics

A Carnot engine operates between a thermal reservoir at 500 K and a sink at 300 K. What is the thermal efficiency of this engine?

  1. 20%
  2. 60%
  3. 40% Correct answer.
  4. 67%

Explanation

Carnot efficiency depends only on the absolute source and sink temperatures, η = 1 - T_L/T_H. Substituting gives 1 - 300/500 = 0.40, or 40%.

Question 31Thermodynamics

A closed system receives 50 kJ of heat and performs 20 kJ of work, with negligible changes in kinetic and potential energy. What is the change in internal energy of the system?

  1. 30 kJ Correct answer.
  2. -70 kJ
  3. -30 kJ
  4. 70 kJ

Explanation

For a closed system the first law is Q - W = ΔU when W is the work done by the system. Thus ΔU = 50 - 20 = 30 kJ.

Question 32Thermodynamics

For an ideal gas, the difference between the constant-pressure specific heat and the constant-volume specific heat equals which quantity?

  1. the gas constant R Correct answer.
  2. kR
  3. R ln(T2/T1)
  4. zero

Explanation

Because enthalpy of an ideal gas is u + RT, differentiating with respect to temperature gives c_p - c_v = R, known as Mayer's relation.

Question 33Thermodynamics

Which statement correctly defines the quality of a saturated liquid-vapor mixture?

  1. The ratio of vapor mass to total mixture mass Correct answer.
  2. The ratio of liquid mass to total mixture mass
  3. The ratio of mixture volume to vapor volume
  4. The ratio of saturation temperature to saturation pressure

Explanation

Quality is the mass fraction of vapor in a saturated mixture, x = m_vapor/m_total. It ranges from 0 at saturated liquid to 1 at saturated vapor.

Question 34Thermodynamics

A refrigeration cycle removes 12 kW of heat from the refrigerated space while the compressor draws 4 kW of electric power. What is the coefficient of performance of the cycle?

  1. 0.33
  2. 3.0 Correct answer.
  3. 4.0
  4. 2.0

Explanation

Refrigeration COP is the cooling effect divided by the work input: COP = Q_L/W = 12/4 = 3.0.

Question 35Thermodynamics

Which relation correctly describes an isentropic process for an ideal gas with constant specific heats?

  1. P v^(1/k) = constant
  2. P v^2 = constant
  3. P v^k = constant Correct answer.
  4. P v = constant

Explanation

For an isentropic process in an ideal gas with constant specific heats, P v^k = constant, where k is the specific heat ratio. This follows from combining the adiabatic relation with the ideal gas law.

Question 36Thermodynamics

Which statement correctly describes the entropy of an isolated system undergoing a process?

  1. It remains constant in every real process.
  2. It can never decrease. Correct answer.
  3. It always decreases.
  4. It equals zero at equilibrium.

Explanation

The second law states that the entropy of an isolated system cannot decrease; it increases for irreversible processes and stays constant for reversible ones.

Question 37Thermodynamics

The dew-point temperature of moist air is the temperature at which which of the following occurs?

  1. the wet-bulb temperature falls below the mixture dew point
  2. condensation begins when the air is cooled at constant pressure Correct answer.
  3. the enthalpy of the moist-air mixture reaches a minimum
  4. the water-vapor partial pressure equals the total pressure

Explanation

Cooling moist air at constant pressure raises relative humidity until the vapor partial pressure reaches the saturation pressure, at which point condensation begins. That temperature is the dew point.

Question 38Thermodynamics

An adiabatic compressor has an isentropic efficiency of 80%. If the isentropic specific work required is 100 kJ/kg, what is the actual specific work?

  1. 80 kJ/kg
  2. 120 kJ/kg
  3. 100 kJ/kg
  4. 125 kJ/kg Correct answer.

Explanation

For a compressor, isentropic efficiency is the ideal work divided by the actual work: η = w_s/w_a. Therefore w_a = 100/0.80 = 125 kJ/kg.

Question 39Thermodynamics

An ideal air-standard Brayton cycle operates with a pressure ratio of 8 and air as an ideal gas with k = 1.4. What is the cycle thermal efficiency?

  1. 55%
  2. 36%
  3. 45% Correct answer.
  4. 62%

Explanation

For an ideal Brayton cycle, η = 1 - r_p^(-(k-1)/k). With r_p = 8 and (k-1)/k = 0.2857, 8^0.2857 = 1.81, so η = 1 - 1/1.81 ≈ 0.45.

Question 40Thermodynamics

A steam power cycle receives 3000 kJ/kg of heat in the boiler and rejects 2100 kJ/kg in the condenser. Neglecting pump work, what is the cycle thermal efficiency?

  1. 30% Correct answer.
  2. 43%
  3. 70%
  4. 35%

Explanation

Cycle efficiency is net work divided by heat supplied, and net work equals heat added minus heat rejected. Thus η = (3000 - 2100)/3000 = 0.30.

Question 41Thermodynamics

In an ideal vapor-compression refrigeration cycle, refrigerant enters the compressor as saturated vapor at 240 kJ/kg, leaves the compressor at 280 kJ/kg, and leaves the condenser as saturated liquid at 100 kJ/kg. What is the coefficient of performance?

  1. 3.5 Correct answer.
  2. 2.8
  3. 1.75
  4. 4.5

Explanation

COP equals the refrigerating effect divided by the compressor work: (h1 - h3)/(h2 - h1). Substituting gives (240 - 100)/(280 - 240) = 140/40 = 3.5.

Question 42Thermodynamics

Two moist air streams mix adiabatically. Stream A has a mass flow of 1 kg/s of dry air at a humidity ratio of 0.008, and stream B has 2 kg/s of dry air at a humidity ratio of 0.016. What is the humidity ratio of the mixture?

  1. 0.0107
  2. 0.0160
  3. 0.0120
  4. 0.0133 Correct answer.

Explanation

Adiabatic mixing conserves dry-air mass and water-vapor mass, so the mixture humidity ratio is the mass-flow-weighted average. W = (1×0.008 + 2×0.016)/3 = 0.0133.

Question 43Thermodynamics

Moist air at a total pressure of 101.325 kPa has a water-vapor partial pressure of 1.7 kPa. What is the humidity ratio?

  1. 0.0100
  2. 0.0106 Correct answer.
  3. 0.0104
  4. 0.0170

Explanation

Humidity ratio is W = 0.622 p_w/(P - p_w), using the dry-air partial pressure in the denominator. W = 0.622 × 1.7/(101.325 - 1.7) = 0.0106 kg vapor per kg dry air.

Question 44Thermodynamics

Air expands through an adiabatic nozzle with negligible inlet velocity. The specific enthalpy drop across the nozzle is 40 kJ/kg. What is the exit velocity?

  1. 283 m/s Correct answer.
  2. 245 m/s
  3. 400 m/s
  4. 200 m/s

Explanation

Steady-flow energy balance for an adiabatic nozzle with negligible inlet velocity gives V2 = sqrt(2(h1 - h2)). Converting 40 kJ/kg to 40,000 J/kg, V = sqrt(80,000) ≈ 283 m/s.

Question 45Thermodynamics

Air is heated from 300 K and 100 kPa to 600 K and 200 kPa. Treating air as an ideal gas with c_p = 1.005 kJ/kg·K and R = 0.287 kJ/kg·K, what is the specific entropy change?

  1. 0.697 kJ/kg·K
  2. 0.199 kJ/kg·K
  3. 0.693 kJ/kg·K
  4. 0.498 kJ/kg·K Correct answer.

Explanation

For an ideal gas, Δs = c_p ln(T2/T1) - R ln(P2/P1). Here both ratios are 2, so Δs = (1.005 - 0.287)(0.693) ≈ 0.498 kJ/kg·K.

Question 46Thermodynamics

Refrigerant flows steadily through an adiabatic capillary tube with negligible changes in kinetic and potential energy. Which property remains essentially constant?

  1. Entropy
  2. Temperature
  3. Enthalpy Correct answer.
  4. Pressure

Explanation

With no heat transfer, no work, and negligible kinetic and potential energy changes, the steady-flow energy balance reduces to h1 = h2. A throttling process is therefore isenthalpic.

Question 47Thermodynamics

Methane (CH4) is burned completely with the theoretical amount of air. Using air as 21% O2 and 79% N2 by volume, what is the stoichiometric air-fuel mass ratio, in kg air per kg fuel?

  1. 15.6
  2. 9.5
  3. 17.2 Correct answer.
  4. 24.5

Explanation

CH4 + 2(O2 + 3.76N2) gives 2 × 4.76 = 9.52 kmol air per kmol fuel. Multiplying by the air and fuel molar masses gives (9.52 × 28.97)/16.04 ≈ 17.2 kg air/kg fuel.

Question 48Thermodynamics

A Carnot refrigerator operates between a cold space at 270 K and surroundings at 300 K. What is its coefficient of performance?

  1. 0.90
  2. 9.0 Correct answer.
  3. 10.0
  4. 0.11

Explanation

The Carnot refrigerator COP is T_L/(T_H - T_L). Substituting gives 270/(300 - 270) = 270/30 = 9.0.

Question 49Thermodynamics

Hot and cold water streams mix adiabatically in a steady-flow mixing chamber. Which statement about this process is correct?

  1. The exergy of the mixture exceeds that of the incoming streams.
  2. The mixing is reversible if it occurs slowly enough.
  3. The entropy of the universe increases. Correct answer.
  4. The entropy of the mixture is less than the sum of the inlet entropies.

Explanation

Mixing streams at different temperatures is irreversible, so entropy is generated even in an adiabatic chamber. The second law therefore requires the total entropy of the streams plus surroundings to increase.

Question 50Thermodynamics

Air leaves a compressor at 450 K and enters a regenerator, where it is heated by turbine exhaust at 800 K. If the regenerator effectiveness is 0.8, what is the air temperature entering the combustor?

  1. 680 K
  2. 730 K Correct answer.
  3. 450 K
  4. 800 K

Explanation

Regenerator effectiveness is defined by ε = (T3 - T2)/(T4 - T2), so T3 = T2 + ε(T4 - T2). Thus T3 = 450 + 0.8(800 - 450) = 730 K.