Charles’ law application at constant pressure: A gas has volume 283 cm³ at 10°C. Heated to 20°C at the same pressure, what is its new volume (in cm³)?

Introduction / Context:This is a direct application of Charles’ law, which states that for a fixed amount of ideal gas at constant pressure, volume is proportional to absolute temperature. Conversions must always be done in Kelvin to avoid errors.

Given Data / Assumptions:

• Initial volume V1 = 283 cm³.
• Initial temperature T1 = 10°C = 283 K.
• Final temperature T2 = 20°C = 293 K.
• Pressure is constant; gas amount unchanged; ideal gas assumption.

Concept / Approach:Charles’ law: V ∝ T at constant pressure and moles. Therefore V2 = V1 * (T2 / T1), with T in Kelvin. Celsius values cannot be used directly because the proportionality holds only relative to absolute zero.

Step-by-Step Solution:

Verification / Alternative check:The 10 K rise near room temperature is roughly a 10/283 ≈ 3.5% increase in volume. 3.5% of 283 cm³ is ~9.9 cm³; 283 + 9.9 ≈ 292.9 cm³, agreeing with 293 cm³.

Why Other Options Are Wrong:

• 283: Ignores temperature change.
• 566: Incorrectly doubles the volume (confuses proportionality).
• 141.5: Implies halving volume; not applicable here.
• 301: Overestimates the proportional increase.

Common Pitfalls:Using Celsius instead of Kelvin; assuming linear changes from Celsius degrees; rounding too early.

Final Answer:293