Question

A certain mass of a gas occupies a volume of \(2~\text{dm}^3\) at STP. At what temperature will the volume of the gas become double, keeping the pressure constant?

• A. \(540.15^\circ\text{C}\)
• B. \(400.15^\circ\text{C}\)
• C. \(546.15^\circ\text{C}\)
• D. \(273.15^\circ\text{C}\)

Hint:

At constant pressure, volume of a gas is directly proportional to absolute temperature.

Answer 1

The Correct Option is D

Step 1: Identify the applicable law.
At constant pressure, Charles’ law applies: \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \] Step 2: Write the given values.
At STP, \[ T_1 = 273~\text{K}, \quad V_1 = 2~\text{dm}^3 \] The volume becomes double: \[ V_2 = 4~\text{dm}^3 \] Step 3: Calculate the final temperature.
\[ \frac{2}{273} = \frac{4}{T_2} \Rightarrow T_2 = 546~\text{K} \] Step 4: Convert into degree Celsius.
\[ T_2 = 546 - 273 = 273^\circ\text{C} \]