What will happen to the pressure of a gas if its temperature is reduced to -273oC?

Analysis

The question asks for the effect of reducing the temperature of a gas to $-273^\circ\text{C}$ on its pressure. This relates to the Pressure Law (or Gay-Lussac's Law) and the concept of Absolute Zero.

Concept

The Pressure Law states that for a fixed mass of gas at a constant volume, the pressure ($P$) is directly proportional to its absolute temperature ($T$) measured in Kelvin:

To convert temperature from Celsius ($^\circ\text{C}$) to Kelvin ($K$), we use the formula:

Solution

1. Convert the given temperature to Kelvin: Given $t = -273^\circ\text{C}$ $$T = -273 + 273 = 0\text{ K}$$

2. Apply the Pressure Law: Since $P \propto T$, if the temperature $T$ becomes $0\text{ K}$ (Absolute Zero), the pressure $P$ must also become zero. $$P = k \times 0 = 0$$

At $-273^\circ\text{C}$ (Absolute Zero), the kinetic energy of the gas molecules theoretically becomes zero, meaning they stop moving and exert no force (pressure) on the walls of the container.

Conclusion

When the temperature of a gas is reduced to $-273^\circ\text{C}$, its pressure drops to zero.

Exam Tip

Always remember that in gas law calculations, you must convert Celsius to Kelvin. If you see $-273^\circ\text{C}$ in a physics question, immediately associate it with "Absolute Zero" and "Zero Pressure."