A barometer tube 90 cm long contains some air above mercury. The reading is 74.5 cm when the true pressure is 76 cm and the temperature is `15^(@)C`. If the reading is observed to be 75.8 cm on a day when the temperature is `5^(@)C`, what is the true pressure ?

Explanation

Initial volume of the air,
`V_(1)` = (length of the barometer tube - reading)A
= `(90-74.5)Acm^(3)=(15.5)Acm^(3)`
Initial pressure of the air, `P_(1)` =
True pressure - reading = 76.0 - 74.5 = 1.5 cm
Initial temperature, `T_(1)` = 273 + 15 = 288 K.
Final volume, `V_(2)=(90.0-75.8)A=14.2Acm^(3)`
Final temperature, `T_(2)=273+5=278K`
`(P_(1)V_(1))/T_(1)=(P_(2)V_(2))/T_(2),(1.5xx15.5_(1))/288=(P_(2)xx14.2)/278`
`P_(2)=(1.5xx15.5xx278)/(14.2xx288)=1.58cm`
The pressure = Reading + pressure of the air
= 75.8 + 1.58 = 77.38 cm