Question

For 3 mol of an ideal gas \(\left[ C_{p,m} = \frac{5}{2}R \right]\), being heated from 300 K to 600 K, the change in entropy at constant pressure is

• A. 48.22 J K\(^{-1}\)
• B. 43.22 J K\(^{-1}\)
• C. 33.22 J K\(^{-1}\)
• D. 38.22 J K\(^{-1}\)

Hint:

For an ideal gas, the change in entropy during heating at constant pressure depends on the heat capacity \( C_p \) and the temperature ratio.

Answer 1

The Correct Option is A

The change in entropy (\( \Delta S \)) at constant pressure is given by: \[ \Delta S = n C_p \ln \left( \frac{T_2}{T_1} \right) \] Where: - \( n = 3 \) mol - \( C_p = \frac{5}{2}R = \frac{5}{2} \times 8.314 \, \text{J/mol·K} \) - \( T_1 = 300 \, \text{K} \) - \( T_2 = 600 \, \text{K} \) \[ \Delta S = 3 \times \left( \frac{5}{2} \times 8.314 \right) \times \ln \left( \frac{600}{300} \right) \] \[ \Delta S = 3 \times 20.785 \times \ln 2 \] \[ \Delta S \approx 48.22 \, \text{J/K} \] Final Answer: \[ \boxed{48.22 \, \text{J/K}} \]