Q.The volume of a gas varies linearly with absolute temperature if its pressure is held constant. Suppose the gas does not liquefy even at very low temperatures, at what temperature will the volume of the gas ideally be zero?

Pressure-versus-temperature and volume-versus-temperature graphs for gases (at fixed volume or fixed pressure respectively) are straight lines when temperature is measured in °C, but with a non-zero intercept. Extrapolating these lines backwards (idealising away the fact that real gases actually liquefy first), every gas's line crosses the temperature axis at exactly the same universal point, $-273.15\,°\text{C}$ -- absolute zero, the theoretical lower limit of temperature. This anchors the Kelvin (absolute/thermodynamic) scale, whose zero coincides with absolute zero and whose degree size matches the Celsius degree; modern calibration uses a single fixed point, the triple point of water, defined as exactly 273.16 K. Absolute temperature also makes the classical gas laws take their simple …