For a monatomic ideal gas, what is the ratio of specific heats (Cp/Cv), commonly denoted as gamma?

Introduction / Context:The ratio of specific heats γ = Cp/Cv influences speed of sound, isentropic relations, and compressor/expander performance. For monatomic gases, γ takes a characteristic value based on degrees of freedom from kinetic theory.

Given Data / Assumptions:

• Monatomic ideal gas (e.g., He, Ne, Ar).
• Equipartition of energy applies.

Concept / Approach:For a monatomic gas, translational degrees of freedom = 3. Then Cv = (3/2)R (molar basis) and Cp = Cv + R = (5/2)R. Therefore, γ = Cp/Cv = (5/2)R / (3/2)R = 5/3 ≈ 1.66.

Step-by-Step Solution:

Verification / Alternative check:Experimental values for noble gases at room temperature (e.g., argon) cluster near 1.66, validating the kinetic theory model.

Why Other Options Are Wrong:

• 1.44 and 1.99: Not consistent with monatomic degrees of freedom.
• 1: Would imply Cp = Cv, which is not true for gases.

Common Pitfalls:Confusing monatomic with diatomic gases (which have γ ≈ 1.4 at room temperature) and using the wrong γ in isentropic equations.

Final Answer:1.66