To determine the number of moles of gas present and the values of Cv and Cp, we need additional information. Specifically, we need to know the heat capacities at constant volume (Cv) and constant pressure (Cp) for the gas.
However, I can provide you with a general equation that relates the heat capacities at constant volume and constant pressure for a monatomic ideal gas:
Cp - Cv = nR
where: Cp is the molar heat capacity at constant pressure, Cv is the molar heat capacity at constant volume, n is the number of moles of gas, and R is the ideal gas constant (8.314 J/(mol·K)).
Given that the heat capacity at constant pressure is greater than the heat capacity at constant volume by 29.1 J/K, we can write the equation as:
Cp - Cv = 29.1
Since the gas is monatomic, the molar heat capacity at constant volume (Cv) can be calculated using the equation:
Cv = (3/2)R
Now, with the values of Cv and the given difference between Cp and Cv, we can solve for the number of moles (n) of the gas:
29.1 = Cp - Cv 29.1 = Cp - (3/2)R Cp = 29.1 + (3/2)R
Finally, we can calculate the number of moles of gas (n):
Cp - Cv = nR 29.1 + (3/2)R - (3/2)R = nR 29.1 = nR n = 29.1/R
Substituting the value of the ideal gas constant (R = 8.314 J/(mol·K)) into the equation, we can calculate the number of moles (n) of the gas.