Question

(a) The brass scale of a barometer gives correct reading at `0^(@)C` . Coefficient of linear expansion of brass is `2.0xx10^(-5)//^(@)C` . The barometer reads `75cm` at `27^(@)C` . What is the atmospheric pressure at `27^(@)C` ?
(b) A barometer reads `75.0cm` on a steel scale. The room temperature is `30^(@)C` . The scale is correctly graduated for `0^(@)C ` . The coefficient of linear expansion of steel is `alpha=1.2xx10^(-5)//^(@)C` and the coefficient of volume expansion of mercury is `gamma=1.8xx10^(-4)//^(@)C` . Find the correct atmospheric pressure.

Answer 1

(a) True value=Scale reading `[1+alpha(theta-theta_(0))]`
Here, Scale reading `=75cm`
`theta-theta_(0)=27-0=27^(@)C`
True value `=75[1+2xx10^(-5)xx27]=75.04cm`
(b) True value=Scale reading `[1+alpha(theta-theta_(0))]`
`=75[1+alpha(30-0)]=75[1+1.2xx10^(-5)xx30]`
`=75.04cm`
Let length of mercury column at `0^(@)C` is `l_(0)`
`l_(30)=l_(0)[(1(gamma)/(3)(theta-theta_(0))]=l_(0)[(1+(1.8xx10^(-4))/(3)(30-0)]`
`=1.0018l_(0)`
`1.0018l_(0)=75.027`
`l_(0)=74.89cm` .