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Physics · University

First law, ideal gases and entropy

Use ΔU=Q−W, where W is work done by the system. A different sign convention is possible only when used consistently.

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Prerequisites

Calculus, pressure-volume work and temperature.

Study notes

Convention

Use ΔU=Q−W, where W is work done by the system. A different sign convention is possible only when used consistently.

Ideal gas

For a fixed amount of ideal monatomic gas, U=3nRT/2 in the classical translational model. Absolute temperature must be in kelvin.

Entropy

For a reversible path, dS=δQrev/T. A state-function change may be calculated along a reversible comparison path even when the actual path is irreversible.

Engines

Carnot efficiency is 1−Tc/Th for reversible operation between two reservoirs. Real engines need not reach that upper bound.

Worked examples

A system absorbs 50 J and does 20 J of work. Using ΔU=Q−W, find ΔU.

Subtract work done by the system from heat entering it.

30 J

Which temperature scale belongs in Tc/Th for Carnot efficiency?

The ratio requires absolute thermodynamic temperatures.

Kelvin

Check your understanding

  1. A reversible engine operates between 600 K and 300 K. Find its Carnot efficiency as a fraction.

  2. In a free expansion of an isolated ideal gas into vacuum, what is the external boundary work?

    1. Infinite
    2. Equal to pressure times final volume
    3. Zero
    4. Always positive

  3. For a reversible isothermal heat transfer of 40 J at 20 K, find entropy change.

  4. Why does Q=0 not imply ΔS=0 for every process?

Answers and marking guidance

Answers and marking notes
  1. 0.5

    1−300/600=0.5.

  2. Zero

    The external resisting pressure is zero; isolation also makes Q zero.

  3. 2 J/K

    ΔS=Qrev/T for this stated constant-temperature reversible transfer.

  4. An irreversible adiabatic process can generate entropy internally. Entropy transfer and entropy production are distinct.

    Credit internal entropy generation and the restriction to reversible adiabatic paths for constant entropy.

Further reading and review references

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