Question

A diatomic ideal gas is brought from an initial equilibrium state at (p₁ = 0.50 atm) and (T₁ = 300K) to a final stage with (p₂ = 0.20 atm) and (T₁ = 500K). Use the results of the previous problem to determine the entropy change per mole of the gas.

a) Calculate the entropy change per mole for the given process.
b) The entropy change depends on the specific heat at constant volume.
c) The change in entropy is independent of the process path.
d) The diatomic nature of the gas has no impact on the solution.

Answer 1

To calculate the entropy change per mole of a diatomic ideal gas, you can use the formula ΔS = nCv ln(T₂/T₁) + nR ln(V₂/V₁), where n is the number of moles, Cv is the molar heat capacity at constant volume, T₁ and T₂ are the initial and final temperatures, V₁ and V₂ are the initial and final volumes, and R is the ideal gas constant. For a diatomic gas, Cv can be calculated using the formula Cv = (y/2)R, where y is the ratio of specific heats.

Step-by-step explanation:

The entropy change per mole of a diatomic ideal gas can be determined using the formula:

ΔS = nCv ln(T₂/T₁) + nR ln(V₂/V₁)

Where:

• ΔS is the entropy change per mole
• n is the number of moles of the gas
• Cv is the molar heat capacity at constant volume
• T₁ and T₂ are the initial and final temperatures, respectively
• V₁ and V₂ are the initial and final volumes, respectively
• R is the ideal gas constant

In this case, the gas is diatomic, so the specific heat capacity at constant volume (Cv) can be calculated using the formula: Cv = (y/2)R, where y is the ratio of specific heats. The ratio of specific heats for a diatomic ideal gas is 7/5, so Cv = (7/10)R.