Question

The volume of given mass of a gas at 'x' K is 2 dm\(^3\). What is the new volume of gas at constant pressure, if temperature is increased to 10x K?

• A. 20 dm\(^3\)
• B. \( \frac{1}{4} \) dm\(^3\)
• C. 4 dm\(^3\)
• D. \( \frac{1}{20} \) dm\(^3\)

Hint:

For gases at constant pressure, remember that the volume is directly proportional to the temperature (Charles' Law).

Answer 1

The Correct Option is A

Step 1: Understanding the relationship.
According to Charles' law, for a fixed mass of gas at constant pressure, the volume of the gas is directly proportional to the temperature (in Kelvin). This can be written as: \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \] Where \(V_1\) and \(T_1\) are the initial volume and temperature, and \(V_2\) and \(T_2\) are the final volume and temperature.
Step 2: Applying the values.
Given that the initial temperature is \(x\) K, the initial volume is 2 dm\(^3\), and the final temperature is \(10x\) K, we can calculate the final volume \(V_2\): \[ \frac{2 \, \text{dm}^3}{x} = \frac{V_2}{10x} \] Solving for \(V_2\): \[ V_2 = 20 \, \text{dm}^3 \] Step 3: Conclusion.
The correct answer is (A) 20 dm\(^3\). The volume increases by a factor of 10 when the temperature increases from \(x\) K to \(10x\) K.