Let's solve each question step by step: --- **Question 1: Identify the correct statement.** **Step 1:** Recall how gas flows from subsonic to supersonic speeds in nozzles. - In isentropic flow, to accelerate a gas from subsonic to supersonic, you need a convergent-divergent (De Laval) nozzle. **Explanation:** A convergent-divergent nozzle allows the gas to accelerate to Mach 1 at the throat (the narrowest point), and then to supersonic speeds in the divergent section. --- **Step 2:** Evaluate the other options: - "Independently of the geometry" is incorrect; the nozzle geometry is crucial. - "Convergent nozzle" alone can't achieve supersonic speeds. - "Divergent nozzle" alone can't accelerate subsonic flow to supersonic. **Explanation:** Only the convergent-divergent nozzle enables transition from subsonic to supersonic in isentropic flow. --- **Step 3:** Select the correct statement. **Final Answer (Question 1):** "For a gas to expand isentropically from subsonic to supersonic speeds, it must flow through a convergent-divergent nozzle." --- --- **Question 2: All isentropic flows are adiabatic.** **Step 1:** Recall definitions: - Isentropic: Constant entropy (no heat transfer and reversible). - Adiabatic: No heat transfer. **Explanation:** All isentropic flows are adiabatic, but not all adiabatic flows are isentropic (because adiabatic can be irreversible). --- **Step 2:** Check the statement: - "All isentropic flows are adiabatic." This is **true** by definition. **Explanation:** Isentropic flow = adiabatic + reversible. Thus, all isentropic flows are adiabatic. --- **Step 3:** Select the correct answer. **Final Answer (Question 2):** True ---

The concept used in answering the first question is the behavior of compressible fluid flow through nozzles, specifically the necessity of a convergent-divergent (De Laval) nozzle for transitioning from subsonic to supersonic speeds in an isentropic process. This is because such a nozzle allows the flow to accelerate smoothly to Mach 1 at the throat and then expand to higher Mach numbers in the divergent section, maintaining constant entropy. For the second question, the key concept is the relationship between isentropic and adiabatic processes. Since isentropic processes are both reversible and adiabatic (no heat transfer), all isentropic flows are inherently adiabatic.