'A horizontal uniform glass tube of 100 ~cm , length sealed at both ends contains 10 ~cm mercury column in the middle. The temperature and pressure of air on either side of mercury column are respectively 31^ C and 76 ~cm of mercury. If the air column at one end is kept at 0^ C and the other end at 273^ C , then the pressure of air which is at 0^ C is : (in cm of Hg )

Step-by-step solution

On keeping the temperature of the ends of tube at 0^ C and 273^ C Applying ideal gas equation p₁ V₁ T₁ = p₂ V₂ T₂ = p₃ V₃ T₃ 76 45 (273+31) = p₂ l (273+0) = p₃(90-l) 273+273 76 45 304 = p₂ l 273 = p₃(90-l) 546 array lll & I && II && III array From Part II and III, p₂ l 273 = p₃(90-l) 546 (Mercury column is at rest, so pressure difference, p₂-p₃=0 p₂=p₃ p₂ l 273 = p₂(90-l) 546 2 l=90-l l=30 ~cm From I and II, 76 45 304 = p₂ 30 273 p₂= 76 45 273 30 304 p₂=102.4