Perfect gas relationships – Boyle’s law identification For a perfect gas, which relation expresses Boyle’s law when absolute temperature T is held constant (isothermal process)?

Introduction / Context:
Gas laws summarize limiting behaviours of ideal gases under constrained variables. Boyle’s law pertains to isothermal transformations, relating pressure and volume inversely at constant temperature.

Given Data / Assumptions:

• Ideal (perfect) gas model.
• Isothermal process: T constant.
• State properties p (absolute pressure) and v (specific volume or volume) are used.

Concept / Approach:
From the ideal-gas equation p * v = R * T (per unit mass) or pV = mRT (for a fixed mass), holding T constant implies p * v remains constant for a given mass. Therefore, pressure is inversely proportional to volume in isothermal conditions.

Step-by-Step Solution:
1) Start with pV = mRT.2) For fixed m and T, right side is constant.3) Hence pV = constant → equivalently p ∝ 1 / V.4) Choose the option that states p * v = constant at constant T.

Verification / Alternative check:
Experimental PV diagrams for gases at moderate pressures show hyperbolic isotherms consistent with pv = constant, validating Boyle’s law as an idealization.

Why Other Options Are Wrong:

• v/T constant: that is Charles’s law (isobaric).
• p/T or T/p constants at constant v: these forms relate to Gay-Lussac’s pressure law (isochoric), not Boyle’s.
• p * T constant at constant v: not a standard gas law statement.

Common Pitfalls:
Mixing absolute temperature with Celsius; the gas laws require absolute temperature scales.

Final Answer:
p * v = constant, if T is kept constant