The Carnot Cycle and the Ceiling on Efficiency · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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The best engine allowed

Science · Thermal & Statistical Physics · ages 19-20
Name ______________________   Date ____________
  1. In a Carnot cycle, heat flows only on the two isotherms.

    Circle one:   True   False

  2. Starting with hot isothermal expansion, which sequence completes a Carnot engine cycle?

    • Adiabatic expansion, cold isothermal compression, adiabatic compression
    • Cold isothermal compression, adiabatic expansion, adiabatic compression
    • Adiabatic compression, cold isothermal compression, adiabatic expansion
  3. Th is the hot reservoir temperature and Tc is the cold one. Which expression gives the Carnot efficiency?

    • 1 - Th/Tc, with both temperatures in kelvin
    • Tc/Th, with both temperatures in kelvin
    • 1 - Tc/Th, with both temperatures in kelvin
  4. A student uses 27 °C and 127 °C directly in Tc/Th. What change is needed?

    • Use Celsius temperatures because the gap is fixed.
    • Use kelvin temperatures before taking their ratio.
    • Use the Celsius temperature gap instead of a ratio.
  5. A Carnot engine runs between 600 K and 300 K. Give its efficiency as a decimal.

    Answer: ______________

  6. Why can no engine exchanging heat only with the same two fixed-temperature reservoirs beat Carnot?

    • Its choice of fuel releases more energy than fuels used in every other engine.
    • Its reversibility sets the second-law limit between those reservoirs.
    • Its cycle returns all rejected heat as work without using a cold reservoir.
  7. A Carnot engine between 400 K and 300 K absorbs 800 J of heat per cycle. Give the maximum work in J.

    Answer: ______________

  8. The area enclosed by a clockwise Carnot loop on a pV diagram equals the net work done by the gas per cycle.

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

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  1. True · The hot isotherm absorbs heat and the cold isotherm releases heat. Neither adiabatic leg exchanges heat.
  2. Adiabatic expansion, cold isothermal compression, adiabatic compression · Adiabatic expansion cools the gas. Cold isothermal compression releases heat. Adiabatic compression warms the gas back to its starting state.
  3. 1 - Tc/Th, with both temperatures in kelvin · The Carnot work fraction is one minus the cold-to-hot absolute-temperature ratio.
  4. Use kelvin temperatures before taking their ratio. · Add 273.15 to each Celsius value. The required ratio is 300.15/400.15, not 27/127.
  5. 0.5 · Efficiency = 1 - 300/600 = 1 - 0.5 = 0.5.
  6. Its reversibility sets the second-law limit between those reservoirs. · A better engine could drive a reversed Carnot machine so their only net effect moved heat from cold to hot without work input.
  7. 200 · Maximum efficiency is 1 - 300/400 = 0.25. Maximum work is 0.25 × 800 = 200 J.
  8. True · The clockwise loop has greater expansion work than compression work. Their difference is its enclosed pV area.
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