Question

How are the absolute entropy values of ideal gases at pressures different from 1 atm determined?

Short answer

Question: Calculate the absolute entropy value of an ideal gas, initially at 1 atm and given entropy value S1, when the pressure is changed to a different value P2. Answer: To calculate the absolute entropy value (S2) at the final pressure (P2), follow these steps: 1. Convert the initial pressure (P1) from atm to Pascal: 1 atm = 101,325 Pa. 2. Use the equation for entropy change during an isothermal process for an ideal gas: ∆S = nRln(P2/101325), where n is the number of moles and R is the gas constant (8.314 J/mol K). 3. Add the initial entropy value (S1) to the calculated entropy change (∆S) to determine the absolute entropy value at the final pressure (P2): S2 = S1 + ∆S.

Step-by-step solution

Understand the entropy change for ideal gases

Entropy change for an ideal gas during an isothermal process can be determined using the following equation: ∆S = nRln(P2/P1) Where ∆S is the entropy change, n is the number of moles of the gas, R is the gas constant (8.314 J/mol K), and P1 and P2 are the initial and final pressures respectively.

Initial conditions

We are given that the initial pressure P1 is 1 atm. We need to convert it to the SI unit (Pascal) as other constants are in the SI unit: 1 atm = 101325 Pa

Determine the final pressure

Since we need to determine the absolute entropy values for the ideal gas at pressures different from 1 atm, let P2 be the final pressure in Pascal that we want to calculate the entropy change for.

Calculate entropy change

Using the equation for entropy change during an isothermal process for an ideal gas, we can calculate the entropy change ∆S, keeping in mind that we need the number of moles (n) of the gas: ∆S = nRln(P2/101325)

Calculate the absolute entropy values

To find the absolute entropy value, we can sum the initial entropy value (S1) of the gas at 1 atm and the calculated entropy change ∆S. Keep in mind that to perform this, we will need the initial entropy value (S1) of the gas at 1 atm: S2 = S1 + ∆S where S2 is the absolute entropy value at the final pressure P2.