Final answer:
The change in entropy for an ideal monoatomic gas that is heated and expanded can be calculated in two parts: first for isochoric heating, then for isobaric expansion, and summed to find the total entropy change.
Step-by-step explanation:
The change in entropy (ΔS) of an ideal monatomic gas during a process can be calculated using the fact that ΔS is a state function and can be calculated as the sum of entropy changes for each step of a reversible path connecting the initial and final states. For a monoatomic ideal gas, cvm (heat capacity at constant volume) is given as 3R/2 where R is the ideal gas constant. To find the entropy change when the gas is heated and its volume changes, we can break the process into two steps: an isochoric (constant volume) heating and an isobaric (constant pressure) expansion.
During an isochoric process, the change in entropy can be calculated using the formula ΔS = n*cvm*ln(T2/T1). When the process is isobaric, ΔS = n*cp*ln(V2/V1), where cp is the heat capacity at constant pressure and equals to cvm + R for an ideal gas. Given that the number of moles of the gas is 2, T1 = 300 K, T2 = 600 K, V1 = 2 L, and V2 = 4 L, we can calculate the entropy change for the isochoric and isobaric processes separately and then sum these values to find the total entropy change.