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ORT Physics practice questions

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Question 1Mechanics and Motion

A cyclist rides 240 m due east in 40 s, then 160 m due west in 20 s. What is the magnitude of the cyclist's average velocity for the whole trip?

  1. 0 m/s
  2. 1.33 m/s Correct answer.
  3. 6.67 m/s
  4. 4.00 m/s

Explanation

Average velocity uses total displacement divided by total time. Displacement is 240 m east minus 160 m west, giving 80 m east in 60 s, so the magnitude is 80/60 = 1.33 m/s. Average speed would instead use the 400 m path length, giving 6.67 m/s.

Question 2Mechanics and Motion

On a velocity-time graph, a straight line with negative slope that lies below the time axis represents a body that is:

  1. moving in the negative direction with decreasing speed
  2. moving in the negative direction with increasing speed Correct answer.
  3. moving in the positive direction while slowing down
  4. at rest at a negative position

Explanation

On a velocity-time graph the slope is acceleration and the height is velocity. A negative slope means acceleration is negative, and a negative velocity means motion in the negative direction. Since velocity and acceleration share the same sign, the speed grows.

Question 3Mechanics and Motion

A stone is dropped from rest and falls freely for 3.0 s before hitting the ground. Taking g = 9.8 m/s² and ignoring air resistance, how far does it fall?

  1. 15 m
  2. 29 m
  3. 88 m
  4. 44 m Correct answer.

Explanation

For free fall from rest, distance equals ½gt². Substituting gives 0.5 × 9.8 × 9.0 = 44.1 m, which rounds to 44 m. The speed after 3.0 s would be 29 m/s, but that is a velocity, not a distance.

Question 4Mechanics and Motion

A box slides across a rough floor at constant velocity while a horizontal push of 18 N is applied. What is the magnitude of the kinetic friction force acting on the box?

  1. zero, because the box moves at constant velocity
  2. 18 N Correct answer.
  3. greater than 18 N
  4. less than 18 N but not zero

Explanation

Constant velocity means zero acceleration, so the net horizontal force must be zero. The friction force therefore exactly balances the 18 N push. Friction is not zero merely because the motion is uniform.

Question 5Mechanics and Motion

Two forces act at a point: 6.0 N directed east and 8.0 N directed north. What is the magnitude of the resultant force?

  1. 2.0 N
  2. 10 N Correct answer.
  3. 48 N
  4. 14 N

Explanation

Perpendicular forces combine by the Pythagorean theorem. The resultant magnitude is the square root of 6.0² + 8.0², which is the square root of 100, namely 10 N. Simply adding the values would be valid only for forces along the same line.

Question 6Mechanics and Motion

A car travelling at 20 m/s brakes uniformly and stops in 5.0 s. What is the magnitude of its acceleration?

  1. 2.0 m/s²
  2. 4.0 m/s² Correct answer.
  3. 100 m/s²
  4. 0.25 m/s²

Explanation

Acceleration is the change in velocity divided by the time taken. The change is 20 m/s to zero over 5.0 s, giving 4.0 m/s² in magnitude. The direction of this acceleration opposes the motion.

Question 7Mechanics and Motion

A book rests on a horizontal table. Which statement correctly describes the reaction partner of the normal force that the table exerts on the book?

  1. It is the force the book exerts on the table, acting downward. Correct answer.
  2. It is the weight of the book, acting downward.
  3. It is the weight of the table, acting downward.
  4. It is the friction force between book and table.

Explanation

Newton's third law pairs forces of the same type acting on different bodies. The normal force from table on book pairs with the normal force from book on table. The book's weight is a gravitational force from Earth and is not the reaction partner of a contact force.

Question 8Mechanics and Motion

A 1200 kg car accelerates uniformly from rest to 15 m/s in 6.0 s. What is the magnitude of the net force on the car?

  1. 200 N
  2. 3000 N Correct answer.
  3. 18000 N
  4. 180000 N

Explanation

First find acceleration: 15 m/s divided by 6.0 s gives 2.5 m/s². Newton's second law then gives F = ma = 1200 × 2.5 = 3000 N. Multiplying mass by the final speed instead would incorrectly give 18000.

Question 9Mechanics and Motion

A projectile is launched at an angle to the horizontal with no air resistance. Which statement about its motion is correct?

  1. The vertical acceleration is zero at the highest point of the path.
  2. The horizontal velocity decreases while the vertical velocity increases.
  3. The horizontal velocity stays constant while the vertical velocity changes uniformly. Correct answer.
  4. Both horizontal and vertical velocities stay constant throughout the flight.

Explanation

With air resistance neglected, the only force is weight, which acts vertically. Horizontal acceleration is therefore zero, so horizontal velocity is constant, while vertical velocity changes at the rate g. At the top the vertical velocity is momentarily zero but the vertical acceleration is still g.

Question 10Mechanics and Motion

A satellite moves in a circular orbit around a planet. If the orbital radius is doubled while the planet's mass stays the same, the orbital speed becomes:

  1. twice as large
  2. smaller by a factor of the square root of 2 Correct answer.
  3. half as large
  4. unchanged

Explanation

For a circular orbit, gravitational force provides the centripetal force, giving v² = GM/r. Speed therefore varies as the inverse square root of the radius. Doubling r divides the speed by the square root of 2.

Question 11Mechanics and Motion

A 0.20 kg ball hits a wall horizontally at 8.0 m/s and rebounds along the same line at 6.0 m/s. The contact lasts 0.050 s. What is the magnitude of the average force exerted by the wall on the ball?

  1. 80 N
  2. 8.0 N
  3. 24 N
  4. 56 N Correct answer.

Explanation

Take the initial direction as positive: change in velocity is −6.0 − 8.0 = −14 m/s. The impulse-momentum relation gives average force magnitude mΔv/Δt = 0.20 × 14 / 0.050 = 56 N. Reversing direction means the velocity change has magnitude 14 m/s, not 2 m/s.

Question 12Mechanics and Motion

A 3.0 kg trolley moving at 4.0 m/s collides with a stationary 1.0 kg trolley and they stick together. What is their common speed after the collision?

  1. 3.0 m/s Correct answer.
  2. 4.0 m/s
  3. 1.0 m/s
  4. 2.0 m/s

Explanation

In a perfectly inelastic collision, momentum is conserved but kinetic energy is not. Initial momentum is 3.0 × 4.0 = 12 kg·m/s, and the combined mass is 4.0 kg, giving 3.0 m/s. Retaining 4.0 m/s would violate momentum conservation.

Question 13Mechanics and Motion

A force of 25 N is applied to a lever arm at 0.40 m from a pivot, perpendicular to the arm. What is the torque about the pivot?

  1. 25 N·m
  2. 62.5 N·m
  3. 10 N·m Correct answer.
  4. 0.016 N·m

Explanation

Torque equals force times perpendicular distance from the pivot, so 25 × 0.40 = 10 N·m. If the force were not perpendicular, only its perpendicular component would count.

Question 14Mechanics and Motion

A uniform metre rule is balanced at its centre. A 2.0 N weight hangs 20 cm to the left of the pivot. Where must a 4.0 N weight be hung to keep the rule horizontal?

  1. 20 cm to the right of the pivot
  2. 10 cm to the right of the pivot Correct answer.
  3. 5 cm to the right of the pivot
  4. 40 cm to the right of the pivot

Explanation

For rotational equilibrium the anticlockwise and clockwise moments must be equal. The left moment is 2.0 × 20 = 40 N·cm, so the right distance is 40/4.0 = 10 cm. A heavier weight needs a shorter lever arm.

Question 15Mechanics and Motion

A machine lifts a 200 N load through 1.5 m while the effort moves 5.0 m with a force of 80 N. What is the efficiency of the machine?

  1. 60%
  2. 40%
  3. 100%
  4. 75% Correct answer.

Explanation

Useful work output is 200 × 1.5 = 300 J, and work input is 80 × 5.0 = 400 J. Efficiency is output divided by input, giving 300/400 = 0.75, or 75%. Efficiency cannot exceed 100% for a real machine.

Question 16Mechanics and Motion

A pump raises 30 kg of water through a height of 5.0 m every 10 s. Taking g = 10 m/s², what useful power does the pump deliver?

  1. 15 W
  2. 1500 W
  3. 150 W Correct answer.
  4. 300 W

Explanation

Gravitational potential energy gained per cycle is mgh = 30 × 10 × 5.0 = 1500 J. Power is energy per unit time, so 1500 J / 10 s = 150 W. Forgetting to divide by time gives the larger 1500 W figure.

Question 17Mechanics and Motion

A moving object has kinetic energy of 400 J. If its speed is doubled while its mass stays the same, its kinetic energy becomes:

  1. 800 J
  2. 400 J
  3. 1600 J Correct answer.
  4. 200 J

Explanation

Kinetic energy equals ½mv², so it is proportional to the square of the speed. Doubling the speed multiplies kinetic energy by four, giving 1600 J. Doubling the energy would correspond to multiplying the speed by the square root of 2.

Question 18Mechanics and Motion

A block slides down a frictionless incline of height 2.0 m from rest. Taking g = 9.8 m/s², what is its speed at the bottom?

  1. 6.3 m/s Correct answer.
  2. 9.8 m/s
  3. 4.4 m/s
  4. 19.6 m/s

Explanation

On a frictionless incline, gravitational potential energy converts entirely to kinetic energy, so v² = 2gh. This gives v = square root of (2 × 9.8 × 2.0) = 6.3 m/s. The incline angle does not affect the final speed, only the acceleration along the slope.

Question 19Mechanics and Motion

A spring obeys Hooke's law with a spring constant of 200 N/m. What force is needed to extend it by 0.15 m?

  1. 0.00075 N
  2. 30 N Correct answer.
  3. 1333 N
  4. 200 N

Explanation

Hooke's law states that force equals the spring constant times extension, F = kx. Substituting gives 200 × 0.15 = 30 N. The spring constant alone is the force per metre, not the force for this extension.

Question 20Mechanics and Motion

A body moves in a circle of radius 2.0 m at a constant speed of 6.0 m/s. What is the magnitude of its centripetal acceleration?

  1. 3.0 m/s²
  2. 12 m/s²
  3. 18 m/s² Correct answer.
  4. 36 m/s²

Explanation

Centripetal acceleration is v²/r. Substituting gives 36/2.0 = 18 m/s², directed toward the centre of the circle. Speed is constant, but the direction of velocity changes continuously, so acceleration is not zero.

Question 21Mechanics and Motion

A student measures the time for 20 oscillations of a pendulum as 40.0 s. What is the period of the pendulum?

  1. 40 s
  2. 2.0 s Correct answer.
  3. 0.50 s
  4. 20 s

Explanation

The period is the time for one complete oscillation, so divide the total time by the number of oscillations. Here 40.0 s / 20 = 2.0 s. Reporting the total time would describe the whole run rather than one cycle.

Question 22Mechanics and Motion

A block of mass 5.0 kg rests on a horizontal surface. The coefficient of static friction is 0.40 and g = 10 m/s². What is the minimum horizontal force needed to start the block moving?

  1. 50 N
  2. 20 N Correct answer.
  3. 0.40 N
  4. 2.0 N

Explanation

The maximum static friction equals the coefficient times the normal force. On a horizontal surface the normal force equals the weight, 50 N, so the limiting friction is 0.40 × 50 = 20 N. A force just above this value starts motion.

Question 23Mechanics and Motion

An object is thrown vertically upward with an initial speed of 20 m/s. Taking g = 10 m/s² and ignoring air resistance, how long does it take to reach its highest point?

  1. 20 s
  2. 0.50 s
  3. 2.0 s Correct answer.
  4. 4.0 s

Explanation

At the highest point the vertical velocity is momentarily zero. Using v = u − gt with v = 0 gives t = u/g = 20/10 = 2.0 s. The total flight time back to the launch level would be twice this value.

Question 24Mechanics and Motion

A force of 12 N acts on a 4.0 kg object that is already moving at 3.0 m/s in the direction of the force. What is the object's speed after 2.0 s?

  1. 9.0 m/s Correct answer.
  2. 1.5 m/s
  3. 6.0 m/s
  4. 12 m/s

Explanation

Acceleration is F/m = 12/4.0 = 3.0 m/s². Applying v = u + at gives 3.0 + 3.0 × 2.0 = 9.0 m/s. Ignoring the initial speed would give only the change in velocity, 6.0 m/s.

Question 25Mechanics and Motion

A 60 kg person stands in a lift that accelerates upward at 2.0 m/s². Taking g = 10 m/s², what is the magnitude of the normal force from the floor on the person?

  1. 120 N
  2. 480 N
  3. 600 N
  4. 720 N Correct answer.

Explanation

The net upward force is the normal force minus weight, and this equals ma. So N = mg + ma = 600 + 120 = 720 N. An upward-accelerating lift makes the floor push harder than the person's weight.

Question 26Mechanics and Motion

A cyclist moves along a straight road and her velocity–time graph is a horizontal line above the time axis. Which statement describes her motion?

  1. She remains at rest because the line is horizontal.
  2. She moves with decreasing velocity and negative acceleration.
  3. She moves with increasing velocity and constant acceleration.
  4. She moves with constant velocity and zero acceleration. Correct answer.

Explanation

On a velocity–time graph the vertical coordinate gives velocity, so a horizontal line means the velocity value does not change with time. Acceleration is the gradient of the graph, and a horizontal line has zero gradient, so acceleration is zero. The line lies above the axis, so the velocity is a steady non-zero value rather than zero.

Question 27Mechanics and Motion

A runner completes one lap of a 400 m circular track in 50 s and finishes at the starting point. Which pair of values is correct for the whole lap?

  1. Average speed 8.0 m/s and average velocity 8.0 m/s
  2. Average speed 0 m/s and average velocity 0 m/s
  3. Average speed 8.0 m/s and average velocity 0 m/s Correct answer.
  4. Average speed 0 m/s and average velocity 8.0 m/s

Explanation

Average speed uses the total distance travelled, which is 400 m, divided by 50 s, giving 8.0 m/s. Average velocity uses displacement, and because the runner returns to the starting point the displacement is zero, so the average velocity is zero. Distance and displacement therefore give very different results for a closed loop.

Question 28Mechanics and Motion

An object is released from rest and falls freely near the Earth's surface with negligible air resistance. Taking g = 9.8 m/s², how far does it fall in the first 3.0 s?

  1. 9.8 m
  2. 44 m Correct answer.
  3. 88 m
  4. 29 m

Explanation

For free fall from rest the displacement is s = ½gt², since the initial velocity is zero. Substituting gives s = 0.5 × 9.8 × 3.0² = 0.5 × 9.8 × 9.0 = 44.1 m, which rounds to 44 m. The result grows with the square of the time, not linearly.

Question 29Mechanics and Motion

A vector has a magnitude of 10 N and makes an angle of 30° with the horizontal. What is the magnitude of its horizontal component?

  1. 0 N
  2. 5.0 N
  3. 10 N
  4. 8.7 N Correct answer.

Explanation

The horizontal component of a vector at angle θ to the horizontal is F cos θ. Here 10 × cos 30° = 10 × 0.866 = 8.7 N. The vertical component would be 10 × sin 30° = 5.0 N, so the two components are not equal for this angle.

Question 30Mechanics and Motion

A stone is thrown horizontally at 15 m/s from the top of a 20 m cliff. Taking g = 10 m/s² and ignoring air resistance, how long does the stone take to reach the ground?

  1. 2.0 s Correct answer.
  2. 4.0 s
  3. 1.3 s
  4. 1.5 s

Explanation

The vertical motion is independent of the horizontal launch speed, so the time depends only on the height and g. Using h = ½gt² gives 20 = 5t², so t² = 4 and t = 2.0 s. The horizontal velocity of 15 m/s affects only how far the stone travels sideways, not the fall time.

Question 31Mechanics and Motion

A ball is thrown vertically upward at 20 m/s. Taking g = 10 m/s², what is the ball's displacement from its launch point after 3.0 s?

  1. 15 m upward Correct answer.
  2. 60 m upward
  3. 45 m upward
  4. 5 m upward

Explanation

Using s = ut − ½gt² with upward positive gives s = 20 × 3.0 − 0.5 × 10 × 9.0 = 60 − 45 = 15 m. The positive sign means the ball is still above its launch point, though it has already passed its highest point and is descending. Displacement and total distance travelled are different here.

Question 32Mechanics and Motion

A 1500 kg car travelling at 12 m/s collides with a stationary 500 kg trailer and the two move off together. What is their common speed immediately after the collision?

  1. 3.0 m/s
  2. 12 m/s
  3. 9.0 m/s Correct answer.
  4. 6.0 m/s

Explanation

Momentum is conserved in the collision because no significant external horizontal force acts during contact. Initial momentum is 1500 × 12 = 18000 kg·m/s, and the combined mass is 2000 kg, so the common speed is 18000 ÷ 2000 = 9.0 m/s. Kinetic energy is not conserved in this inelastic collision, so speed must fall.

Question 33Mechanics and Motion

A 0.50 kg ball moving at 6.0 m/s strikes a wall perpendicularly and rebounds at 4.0 m/s along the same line. What is the change in momentum of the ball?

  1. 3.0 kg·m/s away from the wall
  2. 5.0 kg·m/s away from the wall Correct answer.
  3. 1.0 kg·m/s away from the wall
  4. 5.0 kg·m/s toward the wall

Explanation

Taking away from the wall as positive, the initial momentum is 0.50 × (−6.0) = −3.0 kg·m/s and the final is 0.50 × (+4.0) = +2.0 kg·m/s. The change is final minus initial, +2.0 − (−3.0) = +5.0 kg·m/s, directed away from the wall. Reversing direction means the speeds add in the change rather than subtract.

Question 34Mechanics and Motion

A crate is pulled along a rough horizontal floor at constant speed by a horizontal rope. Which statement about the forces on the crate is correct?

  1. The normal force on the crate equals the tension in the rope.
  2. The tension in the rope equals the kinetic friction force in magnitude. Correct answer.
  3. The net force on the crate is directed forward along the rope.
  4. The tension in the rope is greater than the kinetic friction force.

Explanation

Constant velocity means zero acceleration, so by Newton's second law the net horizontal force must be zero. The only horizontal forces are the rope tension forward and kinetic friction backward, so they must be equal in magnitude. The vertical normal force balances the weight, not the tension.

Question 35Mechanics and Motion

Two blocks connected by a light string over a frictionless pulley hang vertically, one of mass 3.0 kg and the other of mass 1.0 kg. Taking g = 10 m/s², what is the magnitude of the acceleration of the blocks?

  1. 2.5 m/s²
  2. 7.5 m/s²
  3. 10 m/s²
  4. 5.0 m/s² Correct answer.

Explanation

For an Atwood machine the acceleration is a = (m₁ − m₂)g / (m₁ + m₂). Substituting gives a = (3.0 − 1.0) × 10 / (3.0 + 1.0) = 20 / 4.0 = 5.0 m/s². The heavier block descends and the lighter rises with this same magnitude of acceleration.

Question 36Mechanics and Motion

A car rounds a flat horizontal bend of radius 50 m. The coefficient of static friction between tyres and road is 0.50 and g = 10 m/s². What is the maximum speed at which the car can take the bend without skidding?

  1. 25 m/s
  2. 250 m/s
  3. 5.0 m/s
  4. 16 m/s Correct answer.

Explanation

On a flat bend the centripetal force is provided by static friction, so mv²/r ≤ μmg, giving v² ≤ μgr. With μ = 0.50, g = 10 m/s² and r = 50 m, v² ≤ 250 and v ≤ about 16 m/s. The mass cancels, so the answer does not depend on the car's mass.

Question 37Mechanics and Motion

A spring of natural length 20 cm hangs vertically. When a 2.0 N weight is hung from it the length becomes 25 cm. What extra weight must be added to make the length 35 cm?

  1. 6.0 N
  2. 2.0 N Correct answer.
  3. 1.0 N
  4. 4.0 N

Explanation

Hooke's law gives extension proportional to load, and the first 2.0 N produces an extension of 5 cm. To reach 35 cm the total extension must be 15 cm, three times 5 cm, so the total load must be 3 × 2.0 = 6.0 N. The extra weight needed is therefore 6.0 − 2.0 = 2.0 N.

Question 38Mechanics and Motion

A uniform beam of weight 200 N and length 4.0 m is pivoted at one end and held horizontally by a vertical force at the other end. What is the minimum magnitude of this force?

  1. 200 N
  2. 50 N
  3. 100 N Correct answer.
  4. 400 N

Explanation

The weight acts at the beam's centre of gravity, 2.0 m from the pivot, giving an anticlockwise moment of 200 × 2.0 = 400 N·m. The holding force acts at 4.0 m, so for balance F × 4.0 = 400, giving F = 100 N. A vertical force at the far end is the most efficient because it maximises the perpendicular distance.

Question 39Mechanics and Motion

A pump lifts 60 kg of water per minute through a height of 10 m and ejects it at 4.0 m/s. Taking g = 10 m/s², what is the minimum output power of the pump?

  1. 100 W
  2. 108 W Correct answer.
  3. 8.0 W
  4. 600 W

Explanation

Each minute the pump supplies gravitational potential energy mgh = 60 × 10 × 10 = 6000 J and kinetic energy ½mv² = 0.5 × 60 × 16 = 480 J, a total of 6480 J. Dividing by 60 s gives 108 W. Both the lifting and the speeding up of the water must be powered.

Question 40Mechanics and Motion

An object moves in a straight line with a constant resultant force acting on it in the direction of motion. Which statement about the object is correct?

  1. Its momentum remains constant while its speed rises.
  2. Its kinetic energy stays constant because the force is constant.
  3. Its momentum increases at a constant rate. Correct answer.
  4. Its acceleration decreases as its speed increases.

Explanation

By Newton's second law a constant resultant force produces a constant acceleration, and impulse equals change in momentum, so momentum changes at a steady rate equal to the force. The speed rises linearly with time while the force acts. A constant force therefore gives steadily increasing momentum and kinetic energy.

Question 41Thermodynamics and Kinetic Theory

A sealed rigid container holds an ideal gas at constant temperature. If the number of gas molecules is doubled while the volume is unchanged, what happens to the pressure?

  1. It quadruples.
  2. It doubles. Correct answer.
  3. It stays the same.
  4. It halves.

Explanation

For an ideal gas at fixed volume and temperature, pressure is directly proportional to the number of moles (pV = nRT). Doubling the molecule count doubles the number density, so the pressure doubles. Temperature is unchanged, so the average kinetic energy per molecule does not change.

Question 42Thermodynamics and Kinetic Theory

Which statement best describes the absolute temperature of an ideal gas in kinetic theory?

  1. It is proportional to the average distance between neighbouring molecules.
  2. It is proportional to the average translational kinetic energy of its molecules. Correct answer.
  3. It is proportional to the total potential energy stored between molecules.
  4. It is proportional to the total number of molecules in the sample.

Explanation

Kinetic theory links absolute temperature to the mean translational kinetic energy per molecule, (3/2)k_BT for a monatomic gas. Temperature is therefore a measure of average molecular motion, not of potential energy, spacing, or particle count.

Question 43Thermodynamics and Kinetic Theory

In an isothermal reversible expansion of an ideal gas, which quantity is zero for the gas?

  1. The heat absorbed by the gas.
  2. The change in entropy of the gas.
  3. The work done by the gas.
  4. The change in internal energy. Correct answer.

Explanation

For an ideal gas, internal energy depends only on temperature, so an isothermal process gives ΔU = 0. By the first law, the heat absorbed then equals the work done by the gas, and entropy increases because the gas expands.

Question 44Thermodynamics and Kinetic Theory

A gas undergoes an adiabatic free expansion into a vacuum inside an insulated rigid container. Which combination correctly describes the process?

  1. No work, heat absorbed, and a temperature rise.
  2. Positive work, no heat transfer, and a temperature drop.
  3. No work, no heat transfer, and unchanged temperature for an ideal gas. Correct answer.
  4. Negative work, heat released, and unchanged temperature.

Explanation

Free expansion into a vacuum involves no external pressure to work against and an insulated wall prevents heat exchange, so Q = 0 and W = 0. Hence ΔU = 0, and for an ideal gas the temperature stays constant even though the process is irreversible and entropy increases.

Question 45Thermodynamics and Kinetic Theory

The mean speed of molecules in an ideal gas is proportional to which combination of absolute temperature T and molar mass M?

  1. MT
  2. (T/M)^(1/2) Correct answer.
  3. T/M
  4. (M/T)^(1/2)

Explanation

Equating average kinetic energy to thermal energy gives (1/2)m<v^2> = (3/2)k_BT, so the root-mean-square speed scales as (T/M)^(1/2). Heavier molecules move more slowly at the same temperature.

Question 46Thermodynamics and Kinetic Theory

A Carnot engine operates between a hot reservoir at 600 K and a cold reservoir at 300 K. What is its maximum thermodynamic efficiency?

  1. 1.00
  2. 0.67
  3. 0.33
  4. 0.50 Correct answer.

Explanation

Carnot efficiency is 1 − T_c/T_h using absolute temperatures, giving 1 − 300/600 = 0.50. No engine operating between these two reservoirs can exceed this value.

Question 47Thermodynamics and Kinetic Theory

Which statement is the correct expression of the second law of thermodynamics for an isolated system?

  1. The temperature of the system always equalises instantly.
  2. The total energy of the system always decreases.
  3. The pressure of the system always remains constant.
  4. The total entropy of the system never decreases. Correct answer.

Explanation

For an isolated system the entropy change is non-negative: it is zero for reversible processes and positive for irreversible ones. Energy is conserved in an isolated system, and neither temperature nor pressure is forced to a fixed value.

Question 48Thermodynamics and Kinetic Theory

In the Maxwell–Boltzmann distribution of molecular speeds, what happens to the distribution curve as temperature increases?

  1. The distribution becomes a single sharp spike at the mean speed.
  2. The peak shifts to lower speed and the curve becomes narrower and taller.
  3. The peak stays at the same speed but the curve becomes flatter.
  4. The peak shifts to higher speed and the curve becomes broader and flatter. Correct answer.

Explanation

Raising the temperature increases the most probable speed and spreads speeds over a wider range, so the normalised curve flattens while its area stays constant. The low-speed tail shrinks and the high-speed tail grows.

Question 49Thermodynamics and Kinetic Theory

For a fixed mass of ideal gas, which pair of variables is directly proportional along an isobaric path?

  1. Volume and absolute temperature. Correct answer.
  2. Pressure and absolute temperature.
  3. Volume and pressure at constant temperature.
  4. Pressure and volume.

Explanation

At constant pressure, Charles's law states V ∝ T with T in kelvin. The other pairs describe isothermal or isochoric behaviour, not an isobaric path.

Question 50Thermodynamics and Kinetic Theory

A heat pump delivers 4 kJ of heat to a warm room while consuming 1 kJ of electrical work. What is its coefficient of performance for heating?

  1. 5
  2. 0.25
  3. 4 Correct answer.
  4. 3

Explanation

The heating COP is the heat delivered divided by the work input, 4 kJ / 1 kJ = 4. The remaining 3 kJ is drawn from the cold outdoor reservoir.