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Physics · lesson 3 of 4

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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Learn the ideas

Prerequisites: Calculus, pressure-volume work and temperature.

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

Example 1

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

Example 2

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

The ratio requires absolute thermodynamic temperatures.

Kelvin

Check your understanding

8 questions

Decimals or fractions are accepted for numeric answers. Proofs and written responses use sample answers and require human marking. This is practice, not a protected examination.

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

Show answer and explanation

30 J

Subtract work done by the system from heat entering it.

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

Show answer and explanation

Kelvin

The ratio requires absolute thermodynamic temperatures.

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

Show answer and explanation

0.5

1−300/600=0.5.

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

Show answer and explanation

Zero

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

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

Show answer and explanation

2 J/K

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

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

Sample answer and marking guidance

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.

7 For a fixed amount of ideal gas in an isothermal process, what is ΔU?

Show answer and explanation

Zero

Ideal-gas internal energy depends only on temperature.

8 State how a consistent sign convention helps audit a first-law calculation.

Sample answer and marking guidance

Declare whether work is done by or on the system, assign signs for each transfer, then check conservation and the physical direction of energy flow.

Credit sign definitions and energy balance.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.