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QPages 77-80: Q8: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q8 Solution: An amount Q of heat is added to a monatomic ideal gas in a…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume a process‑specific molar heat capacity must lie between $C_V$ and $C_P$, but for arbitrary work exchange this is false; use $C=Q/(n\Delta T)$ with $\Delta U=Q-W$ to compute it directly.

An amount Q of heat is added to a monatomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding. Find the molar heat capacity for the process.

Step-by-Step Verified Solution

**Answer:**

C = 3R

. **Step-by-Step Explanation:** Given:

Q

heat added,

W = Q/2

.

\Delta U = Q - W = Q - Q/2 = Q/2

. For monatomic gas:

\Delta U = \frac{3}{2}nR\Delta T \Rightarrow \frac{Q}{2} = \frac{3}{2}nR\Delta T \Rightarrow Q = 3nR\Delta T

. Molar heat capacity:

C = \frac{Q}{n\Delta T} = 3R

[citation:12].

All Questions in this Chapter

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