Question

For a diatomic gas molecule the value of \(C_p\) in \(J mol^{-1} K^{-1}\) is \((R = 8.2 J mol^{-1} K^{-1})\)

• A. 20.5
• B. 41
• C. 10.25
• D. 12.3
• E. 28.7

Hint:

For monatomic gas: \(C_v = 3R/2\), \(C_p = 5R/2\). For diatomic: \(C_v = 5R/2\), \(C_p = 7R/2\).

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
The molar heat capacities for an ideal gas depend on the degrees of freedom. For a diatomic molecule at moderate temperatures, \(C_v = \frac{5}{2}R\) and \(C_p = C_v + R = \frac{7}{2}R\).

Step 2: Detailed Explanation:
Given \(R = 8.2 \, J mol^{-1} K^{-1}\). For a diatomic gas, \(C_p = \frac{7}{2} R\). \[ C_p = \frac{7}{2} \times 8.2 = 3.5 \times 8.2 = 28.7 \, J mol^{-1} K^{-1} \]

Step 3: Final Answer:
The value of \(C_p\) is \(28.7 \, J mol^{-1} K^{-1}\).