First Law Of Thermodynamics

Question

A sealed cylinder of gas absorbs 250 J of heat from a flame while the expanding gas performs 90 J of work on its piston. By how much does the internal energy of the gas increase?

RankGuru · Accepted Answer

By the First Law of Thermodynamics, the heat $Q$ supplied to a system equals the increase in internal energy $\Delta U$ plus the work $W$ done by the system, written as $Q = \Delta \cup + W$. Rearranging gives $\Delta \cup = Q - W$, which isolates the change in the gas's stored energy. Substituting $Q = 250	ext{ J}$ and $W = 90	ext{ J}$ yields $\Delta \cup = 250 - 90 = 160	ext{ J}$. The value 340 J wrongly adds the work instead of subtracting it, which would violate energy conservation. The value 90 J mistakes the work output for the internal energy change. The value 250 J ignores the work done entirely and assumes all heat became internal energy, which is only true at constant volume. As a sanity check, internal energy rises by less than the heat absorbed because part of that energy left the system as expansion work, and 160 J is correctly smaller than 250 J.

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