Question

A gas obeys Charles' law in the temperature range 0--500 K at a given pressure. Its volume changes to zero at temperature of

• A. $273.15^\circ$C
• B. $0^\circ$C
• C. $-273.15^\circ$C
• D. $500$ K

Hint:

Charles’ Law:

• $V \propto T$ at constant pressure.
• Absolute zero is $0~\textK = -273.15^\circ$C.
• Real gases liquefy before reaching this temperature, but Charles’ law predicts zero volume theoretically at absolute zero.

Answer 1

The Correct Option is C

Charles' law: $V \propto T$ (at constant pressure). This means as $T \rightarrow 0$, $V \rightarrow 0$. Theoretically, if volume becomes zero, the corresponding temperature is absolute zero: \[ T = 0~\text{K} = -273.15^\circ\text{C} \] This is the point at which all molecular motion theoretically stops. So, if volume is zero, the temperature must be $-273.15^\circ$C.

Answer 2

Step 1: Understanding Charles' Law
Charles' Law states that at constant pressure, the volume of a given mass of gas is directly proportional to its absolute temperature (in Kelvin). Mathematically, V ∝ T or V/T = constant.

Step 2: Relationship Between Volume and Temperature
According to Charles' Law, if we plot volume (V) against temperature (T) in Kelvin, the graph is a straight line. If this line is extended, the volume theoretically becomes zero at a certain temperature, known as absolute zero.

Step 3: Determining Temperature at Zero Volume
Since the gas obeys Charles' Law from 0 K to 500 K, extrapolating the volume-temperature graph back to zero volume shows that volume approaches zero at 0 K.
0 K in Celsius is calculated as:
Temperature (°C) = Temperature (K) – 273.15 = 0 – 273.15 = –273.15°C.

Step 4: Conclusion
Thus, the volume of the gas theoretically becomes zero at –273.15°C, which corresponds to absolute zero, the lowest possible temperature where gas particles have minimum kinetic energy.