Ideal-gas Charles law application: At constant pressure, to double the volume of a given mass of an ideal gas initially at 27°C, to what temperature (°C) must it be raised?

Introduction / Context:Charles law for ideal gases states that, at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. This principle underlies many heating and expansion calculations for gases in process equipment and lab settings.

Given Data / Assumptions:

• Ideal-gas behavior.
• Initial temperature T1 = 27°C.
• Final volume V2 = 2V1 at the same pressure.
• Absolute temperature in kelvin is required for proportionality.

Concept / Approach:

At constant pressure: V ∝ T(K). Therefore, V2/V1 = T2/T1. Convert Celsius to kelvin by adding 273.15. Doubling volume requires doubling the absolute temperature. After finding the final kelvin temperature, convert back to °C for the answer format.

Step-by-Step Solution:

Verification / Alternative check:

A quick ratio check: if T doubles in kelvin, V must double at constant pressure. The numeric conversion confirms 327°C.

Why Other Options Are Wrong:

270 or 300°C do not reflect doubling to 600 K. 540°C corresponds to 813 K (more than double). 87°C equals 360 K, not double.

Common Pitfalls:

Forgetting to convert to kelvin; attempting to double the Celsius value instead of the absolute temperature value.

Final Answer:

327