Gas Laws and Internal Energy — Interpreting Boyle’s Law Evaluate the statement: “Boyle’s law states that the change of internal energy of a perfect (ideal) gas is directly proportional to the change of temperature.” State whether this statement is correct or incorrect, and recall what Boyle’s law actually asserts.

Introduction / Context:
This question checks conceptual clarity between two different facts in thermodynamics: (1) Boyle’s law and (2) the temperature dependence of internal energy for an ideal gas. Mixing them up is a common error in early coursework.

Given Data / Assumptions:

• Ideal (perfect) gas behavior is assumed.
• Standard definitions: p = pressure, V = volume, T = absolute temperature, U = internal energy.
• No phase change or chemical reactions are involved.

Concept / Approach:
Boyle’s law states that for a fixed mass of an ideal gas at constant temperature (isothermal condition), p * V = constant. The statement in the prompt instead refers to internal energy U being a function only of temperature for an ideal gas, which is another well-known result often attributed to Joule’s law/ideal-gas property: U = U(T). That property is true, but it is not Boyle’s law. Therefore, attributing the internal-energy statement to Boyle’s law is incorrect.

Step-by-Step Solution:
Recall Boyle’s law: at constant T, p * V = constant (isothermal process).Recall ideal-gas internal energy: dU depends only on dT (Joule’s result for ideal gases).Compare: the prompt equates internal-energy dependence with Boyle’s law, which is a mismatch.Conclusion: The statement is incorrect; it confuses two separate results.

Verification / Alternative check:
On a p–V diagram, a Boyle’s-law path is an isotherm (rectangular hyperbola). Internal energy in an ideal gas remains constant along any isotherm because T is constant; however, that is a consequence of U(T), not the definition of Boyle’s law itself.

Why Other Options Are Wrong:
Choosing “Agree” would wrongly attribute the U–T dependence to Boyle’s law. Boyle’s law makes no direct statement about U.

Common Pitfalls:
Conflating names: Boyle’s (p–V at constant T), Charles’ (V–T at constant p), Gay–Lussac’s (p–T at constant V), and Joule’s statement on internal energy for an ideal gas.

Final Answer:
Disagree