Question

For a diatomic gas, CV is measured to be 21.1 J/(molK). What are Cp and γ ? A. 12.8 J/(molK) and 0.61 B. 12.8 J/(molK) and 1.40 C. 12.8 J/(molK) and 1.65 D. 29.4 J/(molK) and 0.72 E. 29.4 J/(molK) and 1.40 F. 29.4 J/(molK) and 1.65

Answer 1

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.

Answer 2

For a diatomic gas, Cv is the molar heat capacity at constant volume, and Cp is the molar heat capacity at constant pressure. Cp = Cv + R, and γ = Cp/Cv. Using the given Cv value of 21.1 J/(molK) and the gas constant R of 8.314 J/(molK), we can calculate Cp as 29.414 J/(molK) and γ as 1.40.

Step-by-step explanation:

For a diatomic gas, Cv is the molar heat capacity at constant volume, and Cp is the molar heat capacity at constant pressure. The relationship between Cp and Cv is given by Cp = Cv + R, where R is the gas constant. In this case, since Cv is given as 21.1 J/(molK), Cp can be calculated as Cp = 21.1 J/(molK) + R.

As for γ, it is the ratio of Cp to Cv. So γ = Cp/Cv.

To calculate the values of Cp and γ, we need the value of R. The value of the gas constant R is 8.314 J/(molK). Using this value, we can calculate Cp as Cp = 21.1 J/(molK) + 8.314 J/(molK) = 29.414 J/(molK). And then γ can be calculated as γ = 29.414 J/(molK) / 21.1 J/(molK) ≈ 1.40.