Final answer:
The change in temperature of 2.00 mol of helium gas when 80.0 J of heat is added to it in a rigid container is calculated to be 3.22 K.
Step-by-step explanation:
The student is asking for the change in temperature of a quantity of helium gas when it is heated in a rigid container, with a specific heat input. Helium is a monatomic gas, and its behavior under such conditions can be predicted by applying the first law of thermodynamics and the equation for the molar specific heat at constant volume for monatomic gases, Cv = 3/2 R, where R is the gas constant.
To determine the change in temperature, the heat capacity must be calculated. Since there are 2.00 mol of helium, and each mole has a heat capacity of 3/2 R, the total heat capacity is 3.00 R. Using the fact that 80.0 J of heat is added, we can calculate:
q = n * Cv * ΔT
80.0 J = 2.00 mol * (3/2 * R) * ΔT
Substitute R = 8.314 J/(mol*K),
80.0 J = 2.00 mol * (3/2 * 8.314 J/(mol*K)) * ΔT
ΔT = 80.0 J / (3.00 * 8.314 J/K)
ΔT = 3.22 K
The change in temperature of the gas is 3.22 K.