Thermodynamics Practice Test — Medium Level

A free 10-question Thermodynamics practice test for Science Olympiad, written at regional and state level. Every question and answer choice is listed below — correct answers and scoring are revealed when you take the timed test.

10 questions15 min timedMedium levelAI-generated — verify answers against reliable sources

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1. Two samples of water are mixed in an insulated container. One sample is 200 g of water at 80°C, and the other is 100 g of water at 20°C. Assuming no heat is lost to the surroundings and the specific heat of water is the same for both samples, what is the final equilibrium temperature of the mixture?

A.A) 50°C
B.B) 60°C
C.C) 65°C
D.D) 70°C

2. A student is designing an insulated container to keep hot water warm for as long as possible. Which design change would most directly reduce heat loss by conduction?

A.A) Adding a shiny aluminum foil layer on the inner wall
B.B) Filling the space between two walls with still air instead of solid plastic
C.C) Placing the container on a metal table instead of a wooden one
D.D) Painting the outside of the container matte black instead of glossy white

3. Which statement best illustrates the Zeroth Law of Thermodynamics in the context of how a thermometer works?

A.A) A thermometer has a low specific heat so it requires little energy to change its temperature.
B.B) If a thermometer is in thermal equilibrium with an object, and the object is in thermal equilibrium with the room, then the thermometer and the room are at the same temperature.
C.C) The total energy of the thermometer–object system is conserved during heat exchange.
D.D) The entropy of the thermometer always increases as it is brought into contact with hotter objects.

4. A 2.0 mol sample of an ideal gas is at 300 K and 1.5 atm. The gas undergoes an isothermal expansion until its pressure is 0.75 atm. What is the final volume of the gas? (Use R ≈ 0.0821 L·atm/mol·K.)

A.A) 16 L
B.B) 33 L
C.C) 49 L
D.D) 66 L

5. An ideal gas expands isobarically at 1.0 atm from 2.0 L to 5.0 L. How much work is done by the gas during this process? (1.0 atm = 1.01 × 10⁵ Pa, 1.0 L = 1.0 × 10⁻³ m³.)

A.A) 100 J
B.B) 200 J
C.C) 300 J
D.D) 500 J

6. A reversible (Carnot) heat engine operates between a hot reservoir at 500 K and a cold reservoir at 300 K. What is the maximum possible efficiency of this engine?

A.A) 20%
B.B) 40%
C.C) 60%
D.D) 80%

7. A heat engine absorbs 800 J of heat from a hot reservoir and expels 500 J of heat to a cold reservoir each cycle. Which statement is correct about this engine?

A.A) It does 300 J of work per cycle and has an efficiency of 37.5%.
B.B) It does 300 J of work per cycle and has an efficiency of 62.5%.
C.C) It does 500 J of work per cycle and has an efficiency of 37.5%.
D.D) It does 1300 J of work per cycle and has an efficiency of 61.5%.

8. A 2.0 m long metal rod has a linear coefficient of thermal expansion α = 1.2 × 10⁻⁵ K⁻¹. If its temperature increases by 50 K, approximately how much does its length change?

A.A) 0.12 mm
B.B) 0.60 mm
C.C) 1.2 mm
D.D) 6.0 mm

9. Two identical metal plates with the same emissivity and surface area are heated to different uniform temperatures. Plate X is at 300 K and plate Y is at 600 K. According to the Stefan–Boltzmann law, how does the power radiated by plate Y compare to that of plate X?

A.A) Plate Y radiates twice as much power as plate X.
B.B) Plate Y radiates four times as much power as plate X.
C.C) Plate Y radiates eight times as much power as plate X.
D.D) Plate Y radiates sixteen times as much power as plate X.

10. A beaker of ice–water is slowly heated on a hot plate at a constant rate of energy input. Which graph best describes the temperature of the contents of the beaker as a function of time from the start of heating until all the ice has melted and the water has warmed well above 0°C?

A.A) A straight line with constant positive slope the entire time.
B.B) A horizontal line at 0°C the entire time, because the mixture stays at the freezing point.
C.C) A horizontal segment at 0°C while ice is melting, followed by a line with positive slope once only liquid water remains.
D.D) A line that decreases slightly at first, then increases rapidly once the ice begins to melt.