A barometer tube contains some air above mercury and its length is 90 cm. On some hot days when temperature is `50^@C` and true atmospheric pressure is 75 cm of Hg, the reading of the mercury level is 74.8 cm. If the reading is observed to be 75.1 cm on some another day when temperature is `25^@C`, then the true pressure on that day will be ________ cm of Hg

Answer

75.59

Explanation

`P_1 = 75 - 74.8= 0.2 cm` of Hg
The length of barometer tube above mercury level is equivalent to volume of air in the tube in both cases.
`:. V_(1) =90 - 74.8= 15.2 and V_2 = 14.9`
From equation of state, `(P_1V_1)/T_1 = (P_2V_2)/T_2`
( `:. ` number of moles of gas is constant in the barometer tube)
`:. (0.2xx15.2)/((50+273))= (P_2xx14.9)/((25+273))`
`:. P_2 = (298 xx0.2 xx15.2)/(323 xx14.9)= (298xx152xx0.2)/(323xx149)`
`= (2xx8xx0.2)/(17)`
`= (3.2)/17`
`:. P_(2) = 0.188 = 0.19`
`:. P. = 0.188 = 0.19`
`:. P. = 75.4 + 0.19 ~~ 75.59 ` of Hg