First Law Of Thermodynamics

According to NCERT Class 11, Chapter 12 (Thermodynamics), the First Law of Thermodynamics is a statement of energy conservation and is written as $$\begin{gathered} \Delta Q=\Delta \\ cup+\Delta W \end{gathered}$$, 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 $$\begin{gathered} \Delta \\ cup=\Delta Q-\Delta W \end{gathered}$$. Substituting the given values: $$\begin{gathered} \Delta \\ cup=500-200=300 \end{gathered}$$ 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.