### Related Formula From the Ideal Gas Law: PV = nRT$PV = nRT$ According to the First Law of Thermodynamics: Delta Q = Delta U + W$\Delta Q = \Delta U + W$ ### Core Logic The question states that pressure increases linearly with temperature, which means their ratio is constant : P = kT implies fracPT = textconstant$P = kT \implies \frac{P}{T} = \text{constant}$ Since fracPT = fracnRV$\frac{P}{T} = \frac{nR}{V}$, the volume V$V$ must remain constant throughout the process. This identifies it as an isochoric process (Statement E is true). ### Step 1: Evaluate All Statements * Statement A: True. In an isochoric process, dV = 0 implies W = int P dV = 0$dV = 0 \implies W = \int P dV = 0$. * Statement B: False. Since work is zero, the First Law simplifies to Delta Q = Delta U$\Delta Q = \Delta U$, meaning heat added equals the change in internal energy. * Statement C: False. Volume is constant, so it does not increase. * Statement D: True. As pressure increases linearly with temperature, temperature increases, which causes the internal energy of the gas to increase. ### Step 2: Final Selection Gathering the true statements (A, D, and E) points directly to Option (2). ### Pattern Recognition A linear P-T$P-T$ line passing through the origin always indicates a constant volume graph. For constant volume graphs, work done is zero, which simplifies the first law calculation. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Thermodynamics