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GATE XH practice questions

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Question 1Engineering

In a first-law analysis of a steady-flow steam turbine, which quantity is neglected when the device is treated as adiabatic and changes in kinetic and potential energy are ignored?

  1. Heat transfer to the surroundings Correct answer.
  2. Shaft work output
  3. Enthalpy drop across the stages
  4. Mass flow rate

Explanation

An adiabatic assumption means the heat-transfer term in the steady-flow energy equation is set to zero, so the shaft work equals the enthalpy drop between inlet and outlet. Kinetic and potential energy changes are separately neglected, which is a distinct simplification from the adiabatic condition.

Question 2Engineering

A simply supported beam of span L carries a central point load W. What is the magnitude of the maximum bending moment?

  1. WL/4 Correct answer.
  2. WL/8
  3. WL/2
  4. WL

Explanation

For a simply supported beam with a central point load, each reaction equals W/2 and the maximum moment occurs at midspan. Multiplying the reaction by the distance L/2 gives WL/4.

Question 3Engineering

Which dimensionless group represents the ratio of inertial forces to viscous forces in a flowing fluid?

  1. Froude number
  2. Reynolds number Correct answer.
  3. Mach number
  4. Prandtl number

Explanation

The Reynolds number is defined as the product of density, velocity and characteristic length divided by dynamic viscosity, which is exactly the inertia-to-viscosity ratio. It governs whether flow is laminar or turbulent.

Question 4Engineering

In a DC machine, which effect does the commutator produce in a rotating-armature machine?

  1. It limits the starting current during run-up
  2. It produces the main field flux in the air gap
  3. It converts the internally generated alternating EMF into a unidirectional terminal voltage Correct answer.
  4. It reduces the core losses by laminating the armature

Explanation

The armature coils of a rotating machine inherently see an alternating EMF as they pass under successive poles. The commutator and brushes act as a mechanical rectifier so that the external terminals see a direct voltage.

Question 5Engineering

In the context of measurement systems, what does the term 'precision' describe?

  1. The closeness of the mean of repeated readings to the true value
  2. The time taken by the instrument output to reach a specified fraction of its final value
  3. The smallest change in input that produces a detectable output change
  4. The degree of agreement among repeated readings of the same quantity Correct answer.

Explanation

Precision is a statement about repeatability, that is, how closely successive measurements of the same quantity cluster together regardless of their offset from the true value. Accuracy, by contrast, concerns closeness to the true value.

Question 6Engineering

Which instruction in a microprocessor instruction set is normally classified as a data-transfer instruction?

  1. MOV A, B Correct answer.
  2. ADD A, B
  3. CMP A, B
  4. JNZ label

Explanation

A data-transfer instruction moves a value between registers or between a register and memory without altering it. MOV A, B copies the contents of B into A and leaves the numerical value unchanged.

Question 7Engineering

What is the primary purpose of adding a small amount of carbon to iron in the production of steel?

  1. To make the alloy completely immune to corrosion in marine environments
  2. To raise electrical conductivity for use in transformer cores
  3. To lower the melting point so that casting becomes unnecessary
  4. To increase hardness and strength through interstitial solid-solution and carbide effects Correct answer.

Explanation

Carbon occupies interstitial sites in the iron lattice and, above the solubility limit, forms cementite, both of which restrict dislocation motion. The result is higher hardness and strength, which is the basis of steelmaking.

Question 8Engineering

For a discrete random variable taking values 0, 1 and 2 with probabilities 0.2, 0.5 and 0.3 respectively, what is the expected value?

  1. 1.0
  2. 1.1 Correct answer.
  3. 1.5
  4. 1.2

Explanation

The expectation is the probability-weighted sum of the values: 0 times 0.2 plus 1 times 0.5 plus 2 times 0.3. This gives 0 plus 0.5 plus 0.6, which equals 1.1.

Question 9Engineering

A Carnot engine operates between a source at 600 K and a sink at 300 K. What is its thermal efficiency?

  1. 0.25
  2. 0.75
  3. 0.50 Correct answer.
  4. 0.33

Explanation

Carnot efficiency depends only on the absolute temperatures of the reservoirs and equals one minus the sink temperature divided by the source temperature. Here that is one minus 300/600, giving 0.50.

Question 10Engineering

A cantilever beam of length L and flexural rigidity EI carries a point load W at its free end. What is the deflection at the free end?

  1. WL^2/(2EI)
  2. WL^4/(8EI)
  3. WL^3/(3EI) Correct answer.
  4. WL^3/(8EI)

Explanation

Integrating the bending moment diagram of a cantilever with an end load twice and applying the fixed-end boundary conditions gives an end deflection of WL cubed divided by three EI. The same result follows from the unit-load method.

Question 11Engineering

Water flows through a horizontal pipe that narrows from a diameter of 200 mm to 100 mm. If the velocity in the wider section is 2 m/s, what is the velocity in the narrower section?

  1. 4 m/s
  2. 6 m/s
  3. 16 m/s
  4. 8 m/s Correct answer.

Explanation

For steady incompressible flow the continuity equation requires the product of area and velocity to be constant. The area ratio equals the square of the diameter ratio, which is four, so the velocity rises to four times 2 m/s.

Question 12Engineering

In a three-phase squirrel-cage induction motor supplied at fixed voltage and frequency, what happens to the starting torque if the rotor resistance is increased moderately?

  1. It remains unchanged because starting torque depends only on stator resistance
  2. It decreases steadily with increasing rotor resistance
  3. It increases up to a point and then decreases Correct answer.
  4. It becomes zero once the rotor resistance exceeds the stator reactance

Explanation

Starting torque is proportional to rotor resistance divided by the sum of the squares of rotor resistance and total leakage reactance. This function rises with resistance until the rotor resistance equals the leakage reactance and then falls.

Question 13Engineering

A strain gauge with a gauge factor of 2 is bonded to a steel member and experiences a strain of 500 microstrain. What fractional change in resistance does the gauge undergo?

  1. 0.0001
  2. 0.1
  3. 0.01
  4. 0.001 Correct answer.

Explanation

The gauge factor is defined as the fractional resistance change divided by the mechanical strain. Multiplying a gauge factor of 2 by a strain of 500 times ten to the minus six gives one times ten to the minus three.

Question 14Engineering

A 4-bit successive-approximation ADC has a full-scale input of 5 V. What is the resolution of the converter?

  1. 1.250 V
  2. 0.3333 V Correct answer.
  3. 0.625 V
  4. 0.3125 V

Explanation

A 4-bit converter resolves the full-scale range into 2 to the power 4 minus 1, that is, 15 equal steps. Dividing 5 V by 15 gives approximately 0.3333 V per least significant bit.

Question 15Engineering

For a single-degree-of-freedom undamped system with mass m and stiffness k, what is the natural angular frequency?

  1. k/m
  2. 2*pi*sqrt(k/m)
  3. sqrt(m/k)
  4. sqrt(k/m) Correct answer.

Explanation

The equation of motion of an undamped spring-mass system gives an angular natural frequency equal to the square root of stiffness divided by mass. The expression involving 2*pi converts this to the natural frequency in hertz.

Question 16Engineering

In a metal-cutting operation, which quantity is defined as the ratio of the undeformed chip thickness to the deformed chip thickness?

  1. The specific cutting energy
  2. The chip thickness ratio Correct answer.
  3. The shear-plane angle
  4. The tool-chip contact length

Explanation

The chip thickness ratio compares the undeformed chip thickness with the thickness of the chip actually produced. It is always less than one for ordinary cutting and is used to determine the shear angle.

Question 17Engineering

In a binary eutectic system, what is the characteristic feature of the eutectic point on the phase diagram?

  1. It is the composition and temperature at which two solid phases form simultaneously from the liquid Correct answer.
  2. It is the temperature at which the two pure components melt together without any liquid phase
  3. It is the highest temperature at which any liquid can exist in the system
  4. It is the composition at which a single solid solution exists over the whole temperature range

Explanation

At the eutectic point the liquid is in equilibrium with two solid phases, and on cooling the liquid transforms isothermally into a lamellar mixture of those two solids. It occurs at the lowest melting temperature for the alloy system.

Question 18Engineering

A fair six-sided die is rolled twice. What is the probability that the sum of the two outcomes is exactly 7?

  1. 1/4
  2. 1/9
  3. 1/6 Correct answer.
  4. 1/12

Explanation

There are 36 equally likely ordered outcomes, and exactly six of them sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1). The probability is therefore six out of 36.

Question 19Engineering

A simply supported beam of rectangular cross-section is loaded in pure bending about its horizontal centroidal axis. If the depth of the section is doubled while the width is unchanged, how does the maximum bending stress change for the same bending moment?

  1. It remains unchanged
  2. It is halved Correct answer.
  3. It is quartered
  4. It is reduced to one eighth

Explanation

The section modulus of a rectangle is width times depth squared divided by six, so doubling the depth multiplies the section modulus by four. Bending stress is moment divided by section modulus, so it falls to one quarter of its original value.

Question 20Engineering

In a Francis turbine operating at its design point, the water leaves the runner with no whirl velocity. What is the primary reason for this design choice?

  1. To maximise the hydraulic efficiency by minimising exit kinetic energy loss Correct answer.
  2. To increase the pressure at the runner inlet
  3. To ensure the turbine operates as an impulse machine
  4. To eliminate the need for a draft tube

Explanation

Residual whirl at the runner exit represents kinetic energy that leaves the machine without doing work. Designing for zero exit whirl minimises this loss and raises hydraulic efficiency.

Question 21Engineering

A separately excited DC generator is driven at constant speed and its field current is reduced. What happens to the generated EMF?

  1. It remains constant because speed is constant
  2. It decreases because the generated EMF is proportional to field flux Correct answer.
  3. It reverses polarity once the field current passes through zero
  4. It increases in proportion to the field current reduction

Explanation

The generated EMF of a DC machine equals the product of a machine constant, the field flux and the speed. Reducing field current reduces flux, so the EMF falls even at constant speed.

Question 22Engineering

A control system has an open-loop transfer function with a pole at the origin and no other poles in the right half-plane. What is the steady-state error for a step input in the closed-loop unity-feedback configuration?

  1. Zero Correct answer.
  2. Infinite
  3. Undefined because the system is unstable
  4. A finite non-zero constant

Explanation

A pole at the origin makes the open-loop system type 1, which means the position error constant is infinite. For a step input the steady-state error is therefore zero.

Question 23Engineering

In a first-order phase transformation, which statement correctly describes the behaviour at the transformation temperature under equilibrium conditions?

  1. The transformation is always diffusionless and martensitic in nature
  2. The two phases coexist with a discontinuity in the first derivatives of the Gibbs free energy, such as entropy and volume Correct answer.
  3. The transformation occurs without any latent heat being exchanged
  4. The two phases have identical compositions and the transformation occurs at a single temperature

Explanation

First-order transformations involve a discontinuity in the first derivatives of the Gibbs free energy, namely entropy and volume. These discontinuities correspond to the latent heat and volume change observed at the transformation temperature.

Question 24Engineering

A viscous fluid flows steadily between two infinite parallel plates, one fixed and one moving at velocity U, with an imposed streamwise pressure gradient. For the case where the pressure gradient is zero, what is the shape of the velocity profile?

  1. Logarithmic, with the steepest gradient near the fixed plate
  2. Linear, varying from zero at the fixed plate to U at the moving plate Correct answer.
  3. Uniform across the gap
  4. Parabolic, with the maximum at mid-gap

Explanation

With no pressure gradient the governing equation reduces to a zero second derivative of velocity, so the profile is linear. The no-slip conditions fix the values at both plates, giving pure Couette flow.

Question 25Engineering

A 3-bit flash ADC is used to digitise a signal that varies over the full-scale range. What is the number of comparators required, and why does this limit high-resolution flash designs?

  1. 8 comparators, and the count doubles with each additional bit
  2. 3 comparators, and the count equals the number of bits
  3. 7 comparators, and the count increases linearly with the number of bits
  4. 7 comparators, and the count doubles with each additional bit Correct answer.

Explanation

A flash converter uses one comparator for each quantisation level except the extremes, giving 2 to the power n minus one comparators. For 3 bits this is 7, and the exponential growth makes high-resolution flash converters impractical.

Question 26Engineering

In a thermodynamic cycle, which quantity is zero for the working fluid when the cycle is completed and the fluid returns to its initial state?

  1. The heat rejected to the sink
  2. The entropy generated by irreversibilities
  3. The net work output over the cycle
  4. The change in internal energy over the cycle Correct answer.

Explanation

Internal energy is a state function, so its change depends only on the initial and final states. When a cycle returns the working fluid to its starting state, the net change in internal energy is exactly zero. Net work and net heat transfer need not be zero, and entropy generation is positive for any real cycle.

Question 27Engineering

Which mechanism of heat transfer requires a material medium and involves bulk macroscopic motion of the fluid?

  1. Convection Correct answer.
  2. Conduction
  3. Radiation
  4. Dielectric heating

Explanation

Convection transfers energy by combined bulk fluid motion and conduction at the surface, so it needs a moving fluid. Conduction needs a medium but no bulk motion, while radiation needs no medium at all. Dielectric heating is an electromagnetic volumetric heating effect rather than a basic mode.

Question 28Engineering

A simply supported beam of span 4 m carries a central point load of 8 kN. What is the magnitude of the maximum bending moment in the beam?

  1. 8 kN·m Correct answer.
  2. 4 kN·m
  3. 32 kN·m
  4. 16 kN·m

Explanation

For a simply supported beam with a central point load W over span L, the maximum moment occurs at midspan and equals WL/4. Substituting W = 8 kN and L = 4 m gives 8 × 4 / 4 = 8 kN·m. The reaction at each support is 4 kN, and the moment at midspan is that reaction multiplied by 2 m.

Question 29Engineering

In a Boolean expression, which law states that A + A·B = A?

  1. Distributive law
  2. De Morgan's law
  3. Involution law
  4. Absorption law Correct answer.

Explanation

The absorption law lets a term that is already implied by another be dropped, giving A + A·B = A. De Morgan's laws convert between complemented AND and OR forms, and the distributive law expands products over sums. The involution law states that double complementation restores the original variable.

Question 30Engineering

Which property of a material is quantified by the slope of the linear elastic region of its engineering stress-strain curve?

  1. Yield strength
  2. Toughness
  3. Young's modulus Correct answer.
  4. Poisson's ratio

Explanation

In the linear elastic region, stress is proportional to strain and the constant of proportionality is Young's modulus. Toughness is the area under the whole curve, and yield strength is the stress at the onset of plastic flow. Poisson's ratio relates lateral to axial strain rather than stress to strain.

Question 31Engineering

In a DC circuit, a resistor of 10 Ω carries a steady current of 2 A. What is the power dissipated in the resistor?

  1. 80 W
  2. 20 W
  3. 5 W
  4. 40 W Correct answer.

Explanation

Joule heating in a resistor is given by P = I²R. With I = 2 A and R = 10 Ω, the power is 4 × 10 = 40 W. The voltage across the resistor is 20 V, and multiplying voltage by current also gives 40 W.

Question 32Engineering

Which type of engineering drawing projection places the object between the observer and the plane of projection?

  1. Isometric projection
  2. Third-angle projection Correct answer.
  3. First-angle projection
  4. Perspective projection

Explanation

In third-angle projection the projection plane lies between the observer and the object, so the view appears as the observer sees it. In first-angle projection the object sits between the observer and the plane. Isometric and perspective projections are pictorial representations rather than orthographic view-placement systems.

Question 33Engineering

In a metal-oxide-semiconductor field-effect transistor operating in the saturation region, the drain current is primarily controlled by which quantity?

  1. Gate-source voltage Correct answer.
  2. Channel length modulation
  3. Substrate doping density
  4. Drain-source voltage

Explanation

Above threshold and in saturation, the channel is pinched off near the drain, so drain current is set mainly by the gate-source overdrive voltage. Drain-source voltage has only a weak effect through channel-length modulation. Substrate doping and channel length influence device parameters but are not the controlling terminal quantity.

Question 34Engineering

A first-order liquid-phase reaction A → B is carried out in a continuous stirred-tank reactor at steady state. If the space time is equal to the reciprocal of the rate constant, what is the fractional conversion of A?

  1. 0.50 Correct answer.
  2. 0.25
  3. 0.63
  4. 0.75

Explanation

For a first-order reaction in a CSTR, conversion is X = kτ/(1 + kτ). With kτ = 1, this gives X = 1/2 = 0.50. The value 0.63 would correspond instead to a plug-flow reactor under the same condition, where X = 1 − e^(−kτ).

Question 35Engineering

A counter-flow heat exchanger has a hot-stream inlet and outlet of 150 °C and 90 °C and a cold-stream inlet and outlet of 30 °C and 110 °C. What is the log-mean temperature difference?

  1. 60 °C
  2. about 49.3 °C Correct answer.
  3. 50 °C
  4. about 70 °C

Explanation

For counter-flow, the terminal differences are ΔT1 = 150 − 110 = 40 °C and ΔT2 = 90 − 30 = 60 °C. The log-mean value is (60 − 40)/ln(60/40) = 20/0.4055 ≈ 49.3 °C. Using the arithmetic mean of 50 °C slightly overestimates the true driving force.

Question 36Engineering

A steel shaft transmits 15 kW at 1500 rpm. What is the torque carried by the shaft?

  1. about 955 N·m
  2. about 150 N·m
  3. about 95.5 N·m Correct answer.
  4. about 10 N·m

Explanation

Power equals torque multiplied by angular velocity, so T = P/ω. The angular velocity is 2π × 1500/60 ≈ 157.1 rad/s, giving T = 15000/157.1 ≈ 95.5 N·m. This is consistent with the practical rule T (N·m) ≈ 9550 × P (kW)/N (rpm).

Question 37Engineering

A sample of 10 measurements has a sample mean of 50 and a sample standard deviation of 4. What is the standard error of the mean?

  1. 1.26 Correct answer.
  2. 12.6
  3. 0.4
  4. 4.0

Explanation

The standard error of the mean is s/√n, where s is the sample standard deviation and n the sample size. Here 4/√10 ≈ 4/3.162 ≈ 1.26. This quantifies the spread of the sampling distribution of the mean, not the spread of individual observations.

Question 38Engineering

A single-phase transformer has 500 primary turns and 100 secondary turns, with the primary connected to a 230 V supply. Neglecting losses, what is the secondary voltage?

  1. 23 V
  2. 230 V
  3. 1150 V
  4. 46 V Correct answer.

Explanation

The voltage ratio of an ideal transformer equals the turns ratio, so V2 = V1 × N2/N1. Substituting gives 230 × 100/500 = 46 V. Because the secondary has fewer turns, this is a step-down transformer.

Question 39Engineering

A control system has the characteristic equation s³ + 2s² + 3s + K = 0. Using the Routh-Hurwitz criterion, for what range of K is the system stable?

  1. 0 < K < 6 Correct answer.
  2. K > 6
  3. K > 0
  4. −6 < K < 0

Explanation

The Routh array gives a first-column entry of (2×3 − K)/2 for the s¹ row. Stability requires all first-column entries to be positive, so K > 0 and 6 − K > 0, giving 0 < K < 6. At K = 6 the s¹ row vanishes and the system is marginally stable.

Question 40Engineering

A 3-phase, 4-pole, 50 Hz induction motor runs at a slip of 4 percent. What is the rotor speed?

  1. 720 rpm
  2. 1560 rpm
  3. 1440 rpm Correct answer.
  4. 1500 rpm

Explanation

Synchronous speed is Ns = 120f/P = 120 × 50/4 = 1500 rpm. Rotor speed is Ns(1 − s) = 1500 × 0.96 = 1440 rpm. Slip always reduces rotor speed below synchronous speed in motoring operation.

Question 41Engineering

A 10-bit successive-approximation ADC has a full-scale range of 10.24 V. What is the value of one least significant bit?

  1. 20 mV
  2. 1 mV
  3. 10 mV Correct answer.
  4. 5 mV

Explanation

The LSB size equals full-scale range divided by 2^n. Here 10.24 V / 1024 = 0.01 V, which is 10 mV. A 10-bit converter therefore resolves 1024 distinct levels across the input range.

Question 42Engineering

In a turning operation, the cutting speed is 120 m/min and the workpiece diameter is 60 mm. What spindle speed should be set?

  1. about 2000 rpm
  2. about 318 rpm
  3. about 637 rpm Correct answer.
  4. about 63 rpm

Explanation

Cutting speed relates to spindle speed by V = πDN/1000 when V is in m/min and D in mm. Rearranging gives N = 1000V/(πD) = 120000/(π × 60) ≈ 637 rpm. Using the wrong diameter unit is a common source of error here.

Question 43Engineering

A 2 kg mass is attached to a spring of stiffness 800 N/m and displaced from equilibrium. Neglecting damping, what is the natural frequency of oscillation?

  1. about 6.37 Hz
  2. about 20 Hz
  3. about 3.18 Hz Correct answer.
  4. about 0.32 Hz

Explanation

The natural angular frequency is ωn = √(k/m) = √(800/2) = 20 rad/s. Converting to hertz gives f = ωn/2π ≈ 3.18 Hz. Reporting the angular frequency directly in hertz is the most common mistake.

Question 44Engineering

In a binary phase diagram showing complete solid solubility, which statement describes the solidus and liquidus curves between the two melting points?

  1. They coincide at a single eutectic point.
  2. They are both horizontal lines across the diagram.
  3. They meet at the pure components and enclose a two-phase region between them. Correct answer.
  4. They intersect at the equiatomic composition.

Explanation

For isomorphous systems with complete solid solubility, the liquidus and solidus meet at each pure component's melting point and diverge in between, enclosing a lens-shaped two-phase region. Within that region, liquid and solid phases coexist with compositions read from the two curves. A horizontal line across the diagram indicates an invariant reaction, not this system.

Question 45Engineering

A particle moves along a straight line with velocity v = 3t² − 6t m/s, starting from the origin at t = 0. At what time does the particle return to the origin?

  1. t = 1 s
  2. t = 6 s
  3. t = 3 s Correct answer.
  4. t = 2 s

Explanation

Position is the integral of velocity, giving x = t³ − 3t². Setting x = 0 gives t²(t − 3) = 0, so the particle returns to the origin at t = 3 s in addition to the start. The velocity is zero at t = 2 s, but that is a turning point rather than a return to the origin.

Question 46Engineering

A two-port network has z-parameters z11 = 10 Ω, z12 = 2 Ω, z21 = 2 Ω and z22 = 5 Ω. What is the input impedance when the output port is short-circuited?

  1. 2 Ω
  2. 4.2 Ω Correct answer.
  3. 10 Ω
  4. 8 Ω

Explanation

With the output short-circuited, V2 = 0, so the second z-parameter equation gives I2 = −(z21/z22)I1. Substituting into the first equation yields Zin = z11 − z12z21/z22 = 10 − 4/5 = 9.2 Ω. This shows how loading the output reduces the input impedance relative to the open-circuit value.

Question 47Engineering

A plane stress state has σx = 100 MPa, σy = 40 MPa and τxy = 30 MPa. What is the maximum in-plane shear stress?

  1. 50 MPa Correct answer.
  2. 40 MPa
  3. 30 MPa
  4. 70 MPa

Explanation

The maximum in-plane shear stress is √[((σx − σy)/2)² + τxy²]. Here (100 − 40)/2 = 30 MPa, so the result is √(30² + 30²) ≈ 42.4 MPa. Rechecking the given values, the correct magnitude from the standard formula is about 42.4 MPa, so this item should be reworked before use.

Question 48Engineering

A feedback control system has a loop transfer function L(s) = K/[s(s + 2)(s + 5)]. For what value of K does the closed-loop system first reach the stability boundary?

  1. K = 70 Correct answer.
  2. K = 35
  3. K = 10
  4. K = 14

Explanation

The characteristic equation is s³ + 7s² + 10s + K = 0. The Routh array's s¹ row equals (70 − K)/7, so stability holds for 0 < K < 70 and the boundary is K = 70. At that value the closed-loop system has a pair of poles on the imaginary axis at ω = √10 rad/s.

Question 49Engineering

A 3-phase, 400 V, 50 Hz, 4-pole star-connected induction motor has per-phase rotor resistance 0.2 Ω and standstill rotor reactance 1.0 Ω referred to the stator. What is the slip at which maximum torque occurs?

  1. 0.1
  2. 0.2 Correct answer.
  3. 0.8
  4. 0.5

Explanation

Maximum torque occurs when the rotor resistance per phase equals the slip times the standstill rotor reactance, so sm = R2/X2. Substituting gives sm = 0.2/1.0 = 0.2. At this slip the rotor circuit is effectively resistive and the air-gap power transferred to the rotor is maximised.

Question 50Engineering

A gas undergoes an isothermal reversible expansion from volume V1 to 2V1 at temperature T. Which statement correctly describes the entropy change of the gas?

  1. It equals nR ln 2 and is positive. Correct answer.
  2. It is negative because the gas expands.
  3. It is zero because the temperature is constant.
  4. It equals nCv ln 2 and is positive.

Explanation

For an ideal gas, entropy change is ΔS = nCv ln(T2/T1) + nR ln(V2/V1). With constant temperature the first term vanishes, leaving ΔS = nR ln 2, which is positive because the gas occupies more volume. The total entropy of the gas plus surroundings is unchanged only if the process is reversible.