Process Identification — If p * V Remains Constant, Is the Process Isothermal? A thermodynamic process for a fixed mass of gas is carried out such that the product of pressure and volume (p * V) remains constant throughout. Is it correct to call this an isothermal process?

Introduction / Context:Correctly naming a process from observed relationships between properties is a fundamental skill. For an ideal gas, the relationship p * V = constant is the hallmark of an isothermal process for a fixed mass, directly from the ideal-gas equation p * V = m * R * T.

Given Data / Assumptions:

• Fixed mass of ideal gas; gas constant R is constant.
• Product p * V is maintained constant during the process.
• Quasi-static or otherwise well-defined thermodynamic states.

Concept / Approach:For an ideal gas: p * V = m * R * T. If p * V remains constant for a given m and R, then T must remain constant. A constant temperature process is, by definition, an isothermal process. Heating or expansion (mentioned colloquially) can occur while T stays constant if heat transfer balances boundary work.

Step-by-Step Solution:Write ideal-gas relation: p * V = m * R * T.Given p * V = constant with fixed m, R ⇒ T = constant.A process at constant T is called isothermal ⇒ statement is correct.

Verification / Alternative check:On a p–V diagram, an isotherm is a rectangular hyperbola (p = C/V). Any path that follows p * V = constant traces an isothermal curve for an ideal gas.

Why Other Options Are Wrong:“No” would imply that constant p * V does not imply constant T, which contradicts the ideal-gas relation.

Common Pitfalls:Assuming that “heating” always raises temperature; in isothermal expansion, added heat equals work done, keeping T unchanged.

Final Answer:Yes