Question

The molar specific heat of a monoatomic gas at constant pressure is (Universal gas constant = \( 8.3 \, \text{Jmol}^{-1}\text{K}^{-1} \))

• A. \( 24.9 \, \text{Jmol}^{-1}\text{K}^{-1} \)
• B. \( 20.75 \, \text{Jmol}^{-1}\text{K}^{-1} \)
• C. \( 41.5 \, \text{Jmol}^{-1}\text{K}^{-1} \)
• D. \( 16.6 \, \text{Jmol}^{-1}\text{K}^{-1} \)

Hint:

Remember the coefficients for \( R \) for common gases: Monoatomic (\( C_p = 2.5R \)), Diatomic (\( C_p = 3.5R \)).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
For a monoatomic gas, the degrees of freedom \( f = 3 \). We need to calculate the molar specific heat at constant pressure, \( C_p \).
Step 2: Key Formula or Approach:
1. \( C_v = \frac{f}{2}R \) 2. \( C_p = C_v + R = \left( \frac{f}{2} + 1 \right)R \)
Step 3: Detailed Explanation:
For a monoatomic gas, \( f = 3 \). \[ C_p = \left( \frac{3}{2} + 1 \right) R = \frac{5}{2} R = 2.5 R \] Given \( R = 8.3 \, \text{Jmol}^{-1}\text{K}^{-1} \). \[ C_p = 2.5 \times 8.3 \] \[ C_p = 20.75 \, \text{Jmol}^{-1}\text{K}^{-1} \]
Step 4: Final Answer:
The value is 20.75 \( \text{Jmol}^{-1}\text{K}^{-1} \).