Question

One mole of an ideal monatomic gas, initially at a pressure of 1 atm and a volume of 0.025 m³, , is heated to a final state where the pressure is 2 atm and the volume is 0.04 m^3. The gas constant is 8.31447 J/mol middot K. Determine the change in entropy for this process

Answer 1

The change in entropy of the gas can be determined using the formula ΔS = nRln(V2/V1) + nCvln(T2/T1), applying the ideal gas law to find temperatures, and then solving for ΔS using the given initial and final states.

Step-by-step explanation:

The student has asked how to determine the change in entropy for an ideal monatomic gas that is heated from an initial state of 1 atm and 0.025 m³ to a final state of 2 atm and 0.04 m³. To calculate the change in entropy, we can use the formula for an ideal gas: ΔS = nRln(V2/V1) + nCvln(T2/T1). Here, R is the gas constant (8.314 J/mol·K), n is the number of moles (1 mole in this case), V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures.

Using the ideal gas law, PV = nRT, we can find the initial and final temperatures as T1 = P1V1/(nR) and T2 = P2V2/(nR). Once we have the temperatures, we can plug the values into the entropy change formula. Remember, we need to convert pressures from atm to Pa and volumes from m³ to L if using R in J/mol·K, and temperatures should be in Kelvin.

Note that we assume this process is reversible since entropy is a state function and the path does not affect the final calculation of change in entropy. The change in entropy indicates the amount of disorder introduced to the system during the process of heating the gas.