Final answer:
Given that Cv for a diatomic gas is 21.1 J/(mol·K), Cp can be calculated as 29.4 J/(mol·K) using the relationship Cp = Cv + R, where R is the ideal gas constant. The adiabatic index γ, which is the ratio of Cp to Cv, is approximately 1.40. Thus, the correct answer is option E.
Step-by-step explanation:
The question is asking about the specific heat at constant pressure (Cp) and the adiabatic index (γ) for a diatomic gas given that the specific heat at constant volume (Cv) is 21.1 J/(mol·K). We know from thermodynamics that for an ideal gas, the relationship between Cp and Cv is given as Cp = Cv + R, where R is the ideal gas constant (8.314 J/(mol·K)). Applying this equation:
Cp = 21.1 J/(mol·K) + 8.314 J/(mol·K) = 29.414 J/(mol·K)
This value rounds to 29.4 J/(mol·K), which corresponds to options D and E in the provided choices; however, to determine the correct option, we also need to calculate the adiabatic index (γ), which is the ratio of Cp over Cv (γ = Cp/Cv). Calculating γ:
γ = Cp / Cv = 29.4 J/(mol·K) / 21.1 J/(mol·K) ≈ 1.394
This value is close to the ratio 1.40. Therefore, option E with Cp = 29.4 J/(mol·K) and γ = 1.40 is the correct choice.