BITSAT 2024 Shift 1 Paper

In the cycle $A \rightarrow B \rightarrow C \rightarrow D \rightarrow A$, heat is added to the system during the processes $D \rightarrow A$ (at constant volume) and $A \rightarrow B$ (at constant pressure).Calculating the Heat AddedHeat for Process $D \rightarrow A$ (Constant Volume):For an ideal monoatomic gas, the molar heat capacity at constant volume $C_V$ is given by:$C_V = \frac{3}{2} R$The heat added during this process is:$Q_{DA} = n C_V (\Delta T)_{DA} = \frac{3}{2} n R \Delta T$Heat for Process $A \rightarrow B$ (Constant Pressure):The molar heat capacity at constant pressure $C_p$ is given by:$C_p = \frac{5}{2} R$The heat added during this process is:$Q_{AB} = n C_p (\Delta T)_{AB} = \frac{5}{2} n R \Delta T$Total Heat Supplied The total heat supplied in the cycle is the sum of the heat added during these two processes:$Q = Q_{DA} + Q_{AB}$Substitute the expressions for $Q_{DA}$ and $Q_{AB}$ :$Q = \frac{3}{2} n R \Delta T + \frac{5}{2} n R \Delta T$Given $n R \Delta T = p \Delta V$, and substituting it:$Q = \frac{3}{2} (p_0 V_0) + \frac{5}{2} (p_0 V_0)$This simplifies to:$Q = \frac{13}{2} p_0 V_0$