Charles’ law — thermal expansion coefficient at constant pressure: According to Charles’ law, all perfect gases change in volume by what fraction of their original volume at 0 °C for each 1 °C rise in temperature at constant pressure?

Introduction / Context:
Charles’ law defines the proportional expansion of an ideal gas with temperature at constant pressure. Expressing the change per degree near 0 °C leads to the classical fraction used in early engineering texts and helps build intuition for the absolute temperature scale.

Given Data / Assumptions:

• Ideal-gas behavior.
• Reference volume is the volume at 0 °C (273 K).
• Small temperature increments around this point at constant pressure.

Concept / Approach:
Charles’ law states V ∝ T at constant p. Using absolute temperature, a 1 K rise from 273 K to 274 K increases volume by approximately 1/273 of the 0 °C volume. Hence, per 1 °C change near 0 °C, the fractional change is about 1/273 of the original volume at 0 °C.

Step-by-Step Solution:
Start with V1 / T1 = V2 / T2 at constant p.Let T1 = 273 K (0 °C), T2 = 274 K; then V2/V1 = 274/273.Hence ΔV / V1 = (274 − 273)/273 = 1/273 per degree Celsius at 0 °C.

Verification / Alternative check:
Over larger ranges, V scales linearly with T: at 100 °C (373 K), V ≈ (373/273) * V_0, consistent with the same proportionality.

Why Other Options Are Wrong:
Fractions 1/27, 1/93, and 1/173 are not consistent with the absolute zero offset and would imply incorrect zero-volume intercepts.

Common Pitfalls:
Using Celsius directly in proportional formulas; forgetting the need to convert to Kelvin to maintain linear proportionality.

Final Answer:
1/273 of the original volume