A 100 cm long glass tube, sealed at both ends, is positioned horizontally with its middle 10 cm containing mercury. Both ends of the tube enclose air at 27^ C under a pressure of 76 cm of mercury. One air column is subsequently maintained at 0^ C and the other at 127^ C . Determine the length of the air column on the cooler side. Neglect any changes in the volume of the mercury and the glass.

Step-by-step solution

Total length of the tube is 100 cm and the length of the mercury column is 10 cm . Total length of the two air columns is 100 - 10 = 90 cm . Initially, the mercury is in the middle, so both air columns have equal lengths of 45 cm at the same temperature and pressure. Thus, the number of moles of air in both columns is equal. Let the length of the air column on the cooler side ( 0^ C = 273 K ) be x . The length of the air column on the hotter side ( 127^ C = 400 K ) is 90 - x . Since the tube is horizontal, the merc