Question

In the given cycle ABCDA, the heat required for an ideal monoatomic gas will be: 
 

• A. \( p_0 V_0 \)
• B. \( \frac{13}{2} p_0 V_0 \)
• C. \( \frac{11}{2} p_0 V_0 \)
• D. \( 4 p_0 V_0 \)

Hint:

For cyclic processes, heat calculation depends on specific heat at constant volume \( C_V \) and constant pressure \( C_P \).

Answer 1

The Correct Option is B

Step 1: {Total heat added during processes DA and AB}
\[Q = n C_V (\Delta T)_{DA} + n C_P (\Delta T)_{AB}\]Step 2: {For an ideal monatomic gas,}
\[C_V = \frac{3}{2} R, \quad C_P = \frac{5}{2} R\]Step 3: {Substitute known values and expressions}
\[Q = \frac{3}{2} (p_0 V_0) + 5 (p_0 V_0)\]\[= \frac{13}{2} p_0 V_0\]Therefore, the heat supplied is \( \frac{13}{2} p_0 V_0 \).