In Stop-To-Think 19.2, what is the sign of work done on the gas when the ideal gas is taken from State 1 to State 2?

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The question asks about the sign of the work done on the gas when an ideal gas is taken from State 1 to State 2 in Stop-To-Think 19.2. First, recall the general relation for work in thermodynamics: W_on_gas = ∫ P dV. The sign of this work depends on how the volume changes during the process. If the gas undergoes expansion (Volume increases from State 1 to State 2), dV > 0 and the integral ∫ P dV is positive for work done by the gas, which means the work done on the gas is negative. In other words, during expansion, the system does work on its surroundings, so the work on the gas has the opposite (negative) sign. If instead the gas is compressed (Volume decreases, dV < 0), the gas is being pushed inward and work is done on the gas by the surroundings, giving a positive value for W_on_gas. Here, the sign would be positive. Without explicit information about whether State 2 has a larger or smaller volume than State 1 (i.e., whether the process is expansion or compression), we cannot definitively assign the sign. The only provided statement—"The work is negative"—would be correct if the process involved expansion (dV > 0). However, if the process involved compression (dV < 0), the work done on the gas would be positive. Additionally, there is a practical concern: the provided data shows an answer list as empty for options. In a typical multiple-choice setup, one would evaluate each listed option. Since no options are present to assess, we cannot systematically rule out alternatives or confirm the single claimed option beyond the general rule about expansion vs compression. This makes the determination dependent on the implied path between State 1 and State 2 in Stop-To-Think 19.2. In summary, the sign of the work done on the gas is not fixed by the information given here; it depends on whether the process from State 1 to State 2 involves expansion (likely yielding negative work on the gas) or compression (yielding positive work on the gas). If the intended scenario is expansion from State 1 to State 2, the statement "The work is negative" would be correct; if the process is compression, it would be incorrect.

PHYS2305-S2025-Nelson Quiz 12 - Chapters 19 (19.1 - 19.7)

In Stop-To-Think 19.2, what is the sign of work done on the gas when the ideal gas is taken from State 1 to State 2?

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