a barometer record 700 mmHg pressure when the atmospheric pressure is 720 mmHg and the barometer records 720 mmHg pressure when the atmospheric pressure is a 750 mmHg what should be the atmospheric pressure when parameter records 750 mmHg

Let pressure that is read from barometer be P . Let this pressure P varies with atmospheric pressure P_a linearly

 

P = m P_a + C

 

where m and C are constants to be determined

 

when atmospheric pressure P_a = 720 mm of Hg , barometer reads P = 700 mm of Hg

 

700 = m 720 + C  .........................(1)

 

when atmospheric pressure P_a = 750 mm of Hg , barometer reads P = 720 mm of Hg

 

720 = m 750 + C  ....................(2)

 

Bysubtracting eqn.(1) from eqn.(2) , we get

 

we get  m = (2/3)

 

By substituting m = (2/3) in eqn.(1) we get C = 220

 

Hence , P_a = ( P - C ) / m

 

If barometer reads P = 750 mm , then P_a = ( 750 - 220 ) × (3/2) = 795 mm of Hg