Question

An ideal gas is heated from \(27^{\circ}\text{C}\) to \(627^{\circ}\text{C}\) at constant pressure. If initial volume of gas is \(4 \text{m}^3\), then the new volume of the gas will be

• A. \(12 \text{m}^3\)
• B. \(6 \text{m}^3\)
• C. \(3 \text{m}^3\)
• D. \(2 \text{m}^3\)

Hint:

Use Charles law with temperatures in kelvin.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
At constant pressure the volume of a fixed amount of an ideal gas is proportional to the absolute temperature: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\).

Step 2: Key Formula or Approach:
Convert to kelvin: \(T_1 = 27 + 273 = 300\) K and \(T_2 = 627 + 273 = 900\) K.

Step 3: Detailed Explanation:
\[ V_2 = V_1\frac{T_2}{T_1} = 4 \times \frac{900}{300} = 12\ \text{m}^3 \]
Using the Celsius values directly would give \(4 \times \frac{627}{27} = 92.9\), which is wrong, so the kelvin scale must be used. The values \(6\), \(3\) and \(2\) m\(^3\) correspond to volume ratios of \(1.5\), \(0.75\) and \(0.5\), which do not match a temperature ratio of \(3\).

Final Answer:
The new volume is \(12\) m\(^3\), option (A). \[ \boxed{12\ \text{m}^3} \]