First Law Applied To Constant Pressure Heating

Based on NCERT Class 11, Chapter 12 (Thermodynamics), the heat supplied at constant pressure is $Q=n{C}_P\Delta T$, where for a monatomic ideal gas $C_V=\frac{3R}{2}$ and by Mayer's relation $C_P=C_V+R=\frac{3R}{2}+R=\frac{5R}{2}$. Substituting $n=2$, $\Delta T=50$ K and $R=8.3$: $C_P=\frac{5\times 8.3}{2}=20.75$ J/mol·K, so $Q=2\times 20.75\times 50=2075$ J. Part of this heat raises internal energy and part does expansion work. The option 1245 J is wrong because it uses $C_V=3R/2$, computing only the internal energy change and ignoring the expansion work at constant pressure. The option 830 J is wrong because it uses $R$ alone times the relevant factors, omitting the specific heat structure. The option 4150 J is wrong because it doubles the correct value, likely using $5R$ instead of $5R/2$. A plausibility check: at constant pressure $Q$ must exceed the constant-volume heat $n{C}_V\Delta T=1245$ J because extra energy goes into work, and indeed $2075>1245$, confirming the answer is consistent.