According to Charle's law, the volume of a gas becomes zero at

Analysis of the Question

This question tests your understanding of Charles's Law and the concept of Absolute Zero. You are being asked to identify the specific temperature at which the theoretical volume of an ideal gas drops to zero.

Concept Explanation

Charles's Law states that the volume ($V$) of a fixed mass of gas is directly proportional to its absolute temperature ($T$) in Kelvin, provided the pressure remains constant. Mathematically, this is expressed as:

Where:

• $V$ = Volume
• $T$ = Temperature in Kelvin (K)
• $k$ = Constant

In the Celsius scale, the relationship is $V = k(t + 273)$, where $t$ is the temperature in degrees Celsius. If we want the volume ($V$) to be zero, the temperature in Kelvin must be $0\text{ K}$.

To convert this to Celsius:

This temperature ($-273^\circ\text{C}$) is known as Absolute Zero. At this point, the kinetic energy of the gas particles is theoretically at its minimum, and the volume of an ideal gas would vanish.

Step-by-Step Solution

1. Recall the formula: $V \propto T$ (where $T$ is in Kelvin).
2. Identify the condition: We are looking for the temperature where $V = 0$.
3. Apply the condition: For $V$ to be $0$, $T$ must be $0\text{ K}$.
4. Convert to Celsius: Since $T(\text{K}) = t(^\circ\text{C}) + 273$, setting $T = 0$ gives: $0 = t + 273$ $t = -273^\circ\text{C}$

Conclusion

The temperature at which the volume of a gas theoretically becomes zero is $-273^\circ\text{C}$.

Exam Tip

Always remember that in gas law calculations (Boyle's Law, Charles's Law, Pressure Law, and the Ideal Gas Equation), you must always convert your temperature from Celsius to Kelvin by adding $273$. Never use Celsius directly in these formulas!