Absolute Zero: MDCAT Chemistry notes

Definition

Absolute zero is the lowest possible temperature, 0 K = −273.15 °C (usually rounded to −273 °C). It is the temperature at which the volume of an ideal gas would theoretically become zero and molecular motion (translational kinetic energy) would cease.

How absolute zero was found

According to Charles's law, at constant pressure a gas's volume changes by $\frac{1}{273}$ of its volume at 0 °C for each degree change:

$$V_t=V_0\left(1+\frac{t}{273}\right)$$

Putting $t=-273$ °C gives $V_t=V_0(1-1)=0$. When volume is plotted against temperature in °C, each gas gives a straight line. Extrapolated back, all the lines cut the temperature axis at −273.15 °C, whatever the gas or the pressure. This common point is absolute zero.

The Kelvin (absolute) scale

Lord Kelvin proposed a temperature scale starting at absolute zero. The starting point of the Kelvin scale is 0 K; there are no negative kelvin temperatures. One kelvin is the same size as one degree Celsius.

$$T(\text{K})=t(^\circ\text{C})+273.15$$

Point	Kelvin	Celsius	Fahrenheit
Absolute zero	0 K	−273.15 °C	−459.67 °F
Freezing point of water	273.15 K	0 °C	32 °F
Boiling point of water	373.15 K	100 °C	212 °F

What happens at absolute zero (ideal gas)

• Volume would be zero (Charles's law).
• Pressure would be zero, since pressure comes from molecular collisions with the walls and molecular motion stops ($P\propto T$ at constant volume).
• Average kinetic energy $\frac{3}{2}kT$ becomes zero.

Why it cannot be reached

Real gases do not follow Charles's law down to 0 K: they liquefy and then solidify well before absolute zero, because intermolecular attractions become important at low temperature. Absolute zero is approached very closely in laboratories but never actually attained.

Worked examples

• Convert −73 °C to kelvin: $-73+273=200$ K.
• Convert 50 K to Celsius: $50-273=-223$ °C.
• A gas occupies 546 cm³ at 273 °C (546 K). Cooling it at constant pressure to 0 °C (273 K) halves its volume to 273 cm³; cooling further towards 0 K would in theory shrink it to zero.

Common MDCAT traps

• Absolute zero is −273 °C, not 0 °C or −173 °C.
• The Kelvin scale starts at 0 K, not at −273.15 K.
• The V-t graph cuts the axis at −273 °C; the V-T (kelvin) graph passes through the origin.
• Both the pressure and the volume of an ideal gas become zero at 0 K.

Quick revision

• 0 K = −273.15 °C.
• Kelvin temperatures are never negative.
• All gases extrapolate to zero volume at the same temperature.
• Real gases liquefy before 0 K.
• K = °C + 273.