CLASSICAL MECHANICS & THERMODYNAMICS - Chapter 7, Exercise 1 Solution
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The First Law with Zero Work (Constant-Volume Heating)

PROBLEM
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A gas in a sealed, rigid container is heated, receiving 800 J of
heat. Because the container is rigid, the gas cannot expand and does
zero work on its surroundings (W = 0). Using the First Law,
calculate the change in the gas's internal energy.

SOLUTION
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Using the First Law:

    delta U = Q - W

Substitute the given values:

    Q = 800 J
    W = 0 J   (rigid container, no expansion possible)

    delta U = 800 - 0
    delta U = 800 J

ANSWER: The gas's internal energy increases by 800 J.

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WHY THIS WORKS AS AN ANSWER

Because the container is rigid, the gas has nowhere to expand into,
so it cannot push against anything and does no mechanical work on its
surroundings at all (W = 0). With no energy leaving the system as
work, every single joule of heat added goes directly into raising the
gas's own internal energy - unlike the chapter's own worked example,
where 200 of the 500 J supplied left the system again as work done on
a moving piston. This is the real physical difference between heating
something at constant volume (all the heat raises internal energy,
typically observed as a temperature rise) versus heating something
that is free to expand (some of the heat is "spent" doing work
instead).