Gas mixture contains 2.50 mol of O2 and 3.00 mol of Ar.
Part A
What is this mixture's molar specific heat at constant volume?
Cv = ________R
Part B
What is this mixture's molar specific heat at constant pressure?
Cp = ________R
To determine the molar specific heat at constant volume (Cv) and constant pressure (Cp) for a gas mixture, we need to know the molar specific heats of the individual gases involved.
Part A:
The molar specific heat at constant volume (Cv) for an ideal gas is given by the equation:
Cv = (n1Cv1 + n2Cv2 + ... + nkCvk) / (n1 + n2 + ... + nk)
where n1, n2, ... nk are the number of moles of the respective gases, and Cv1, Cv2, ... Cvk are their molar specific heats at constant volume.
For oxygen (O2), the molar specific heat at constant volume (Cv1) is approximately 5R, where R is the ideal gas constant.
For argon (Ar), the molar specific heat at constant volume (Cv2) is approximately 3.5R.
To calculate the molar specific heat at constant volume (Cv) for the mixture:
Cv = (2.50 mol * 5R + 3.00 mol * 3.5R) / (2.50 mol + 3.00 mol)
Simplifying the equation:
Cv ≈ (12.50R + 10.50R) / 5.50 mol
Cv ≈ 1.91R
Therefore, the mixture's molar specific heat at constant volume (Cv) is approximately 1.91R.
Part B:
The molar specific heat at constant pressure (Cp) for an ideal gas is related to the molar specific heat at constant volume (Cv) by the equation:
Cp = Cv + R
Therefore, to find Cp for the gas mixture, we can use the value of Cv from Part A and add R to it.
Cp = Cv + R = 1.91R + R = 2.91R
Therefore, the mixture's molar specific heat at constant pressure (Cp) is approximately 2.91R.