Question:
A diatomic gas is heated at constant pressure. What fraction of the heat energy is used to increase the internal energy?
A diatomic gas is heated at constant pressure. What fraction of the heat energy is used to increase the internal energy?
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For monatomic gas: \(C_p/C_v = 5/3\); diatomic: \(7/5\); polyatomic: \(4/3\).
Updated On: Apr 23, 2026
- \(3/5\)
- \(3/7\)
- \(5/7\)
- \(5/9\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the 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: Detailed 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: Final Answer:
Thus, fraction = \(5/7\).
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: Detailed 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: Final Answer:
Thus, fraction = \(5/7\).
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