Final answer:
The gas is polyatomic.
Step-by-step explanation:
The specific heat capacity of an ideal gas depends on the number of particles it contains. Monatomic gases have only one atom per molecule and diatomic gases have two atoms per molecule.
Polyatomic gases have more than two atoms per molecule. The specific heat capacities of monatomic, diatomic, and polyatomic gases are different, and they can be used to determine the type of gas.
In this problem, we can determine the type of gas by considering the change in internal energy during the cooling process. If the gas is monatomic, the change in internal energy can be determined using the equation ΔU = (3/2) nRΔT, where n is the number of moles of gas and ΔT is the change in temperature. If the gas is diatomic or polyatomic, the change in internal energy can be determined using the equation ΔU = (5/2) nRΔT.
By comparing the calculated change in internal energy to the amount of heat removed from the gas (ΔQ = -980 J), we can determine the type of gas.
Let's calculate the change in internal energy for the given cooling process. First, we need to convert the temperatures from °C to Kelvin:
- Initial temperature (T1) = 30.0 °C + 273.15 = 303.15 K
- Final temperature (T2) = -40.0 °C + 273.15 = 233.15 K
Now, we can calculate the change in internal energy:
ΔU = (5/2) nRΔT
where n is the number of moles of gas. From the given information, n = 0.560 mol. The gas constant R is approximately 8.314 J/(mol·K).
Substituting the values into the equation:
ΔU = (5/2) * (0.560 mol) * (8.314 J/(mol·K)) * (233.15 K - 303.15 K)
Calculating the change in internal energy:
ΔU = (5/2) * (0.560 mol) * (8.314 J/(mol·K)) * (-70 K)
Simplifying the equation:
ΔU = - 1227.7 J
We find that the change in internal energy is -1227.7 J. Since the amount of heat removed from the gas is 980 J, which is less than the change in internal energy, we can conclude that the gas is polyatomic.