Internal Energy And First Law

Question

A gas absorbs 450 J of heat and does 120 J of work on the surroundings during an expansion process. What is the change in internal energy of the gas?

RankGuru · Accepted Answer

The First Law of Thermodynamics states that the change in internal energy of a system equals the heat absorbed by the system minus the work done by the system on its surroundings: $\Delta \cup = q - w$. Here, the gas absorbs heat so $q = +450$ J (positive, heat flows into the system). The gas does work on the surroundings during expansion, so $w = +120$ J (work done BY the system is positive). Applying the first law: $\Delta \cup = 450 - 120 = 330$ J. Option 570 J is incorrect because it adds heat and work instead of subtracting work done by the system. Option -330 J would result if the gas were releasing heat instead of absorbing it. Option -570 J arises from both incorrect sign conventions applied simultaneously. This is a core NCERT Chapter 6 application of the first law of thermodynamics. Plausibility check: since heat absorbed exceeds work done, internal energy must increase, confirming $\Delta \cup > 0$.

Internal Energy And First Law

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