First Law Of Thermodynamics

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A gas in a cylinder absorbs 500 J of heat while the gas does 200 J of work in pushing a piston outward, so by how much does its internal energy change?

RankGuru · Accepted Answer

According to NCERT Class 11, Chapter 12 (Thermodynamics), the First Law of Thermodynamics is a statement of energy conservation and is written as $\Delta Q = \Delta \cup + \Delta W$, where $\Delta Q$ is heat supplied to the gas, $\Delta U$ is the change in internal energy, and $\Delta W$ is the work done by the gas. Rearranging gives $\Delta \cup = \Delta Q - \Delta W$. Substituting the given values: $\Delta \cup = 500 - 200 = 300$ J. Because the system absorbs heat ($\Delta Q$ positive) and does work on the surroundings ($\Delta W$ positive), part of the supplied heat leaves as work and the remainder raises the internal energy. The option 700 J is wrong because it incorrectly adds the work instead of subtracting it. The option $-300$ J is wrong as it reverses the sign convention, treating work done by the gas as added to internal energy with the wrong sign. The option 100 J is wrong because it does not follow from the correct subtraction. A plausibility check: $\Delta U$ must be less than $\Delta Q$ whenever the gas does positive work, and 300 J < 500 J confirms the sign and magnitude are reasonable.

First Law Of Thermodynamics

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