Question

A diatomic gas is heated at constant pressure. What fraction of the heat energy is used to increase the internal energy?

• A. \(3/5\)
• B. \(3/7\)
• C. \(5/7\)
• D. \(5/9\)

Hint:

For monatomic gas: \(C_p/C_v = 5/3\); diatomic: \(7/5\); polyatomic: \(4/3\).

Answer 1

The Correct Option is C

Step 1: Concept:
For diatomic gas, \(C_p = \frac{7}{2}R\), \(C_v = \frac{5}{2}R\). At constant pressure, \(Q = nC_p\Delta T\). \(\Delta U = nC_v\Delta T\).
Step 2: Explanation:
Fraction = \(\frac{\Delta U}{Q} = \frac{nC_v\Delta T}{nC_p\Delta T} = \frac{C_v}{C_p} = \frac{\frac{5}{2}R}{\frac{7}{2}R} = \frac{5}{7}\).
Step 3: Conclusion:
Thus, fraction = \(5/7\).