Physics

Physics

Problem

38. The volume of an ideal gas changes as the gas undergoes an isobaric (constant pressure) process starting from temperature `273∘C273{ }^{\circ} \mathrm{C}` and ending at `546∘C546^{\circ} \mathrm{C}`. What is the ratio of the new volume of the gas to the old volume `(Vnew /Vold )\left(\mathrm{V}_{\text {new }} / \mathrm{V}_{\text {old }}\right)` ? (A) `12\frac{1}{2}` (B) `23\frac{2}{3}` (C) `32\frac{3}{2}` (D) 2 (A) `12\frac{1}{2}` (B) `23\frac{2}{3}` (C) `32\frac{3}{2}` (D) 2
Intuitive explanation

In an isobaric process, pressure stays constant, so the ideal gas law tells us that volume and absolute temperature are directly proportional: V∝TV \propto T. The key is converting those Celsius temperatures to Kelvin—273 °C becomes 546 K, and 546 °C becomes 819 K—then taking the ratio of absolute temperatures to find the volume ratio.

Intuitive explanation

In an isobaric process, pressure stays constant, so the ideal gas law tells us that volume and absolute temperature are directly proportional: V∝TV \propto T. The key is converting those Celsius temperatures to Kelvin—273 °C becomes 546 K, and 546 °C becomes 819 K—then taking the ratio of absolute temperatures to find the volume ratio.

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