A horizontal uniform glass tube of `100cm` length is 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 repectively `31^(@)C` and `76cm` of mercury, if the air column at one end is kept at` 0^(@)C` and the other end at `273^(@)C` then pressure if air which is `0^(@)C` is
(in `cm` of `Hg`)

Options

A. 76
B. 68.2
C. 102.4
D. 122

Answer

C

Explanation

Length of air column on both sides is 45 cm when one side is at 0°C and the other is at 273°C.
Pressure must be same on both sides
`l_1/T_1 = l_2/T_2 rArr l_1/273 = I_2/((273 + 273)) rArr l_1 = l_2/2`
As `I_1 + I_2 = 90 cm rArr I_1 = 30 cm , and l_2 = 60 cm `
Gas equation
`(P_1l_1)/T_1 = (PI)/T rArr (P_1 xx 30)/(273) = (76 xx 45)/(273 xx 81) rArr P_1 = 102.5 atm`.