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An ideal gas is trapped between a mercur...

An ideal gas is trapped between a mercury column and the closed-end of a narrow vertical tube of uniform base containing the cloumn. The upper end of the tube is open to the atmosphere. the atmosphric pressure equals 76cm of mercury. the length of the mercuty column and trapped air column are 20 cm and 43 cm respectively. What will be the length of the air column when the tube is tilted slowly in a vertical plane through an angle of `60^(@)`? Assume the temperature to remain constant.

Text Solution

Verified by Experts

Case 1 : Atmospheric pressure + Pressure
due to mercury column
Case 2 : Atmospheric pressure +
Component of the pressure due
to mercury column
`((P_1)(V_1) = (P_2)(V_2))`
` rArr (76 xx (rho_Hg) xx g + (rho_(Hg)) xx g xx 20 ) xx A xx 43`
` = (76 xx(rho_(Hg)) xx g + (rho_ (Hg)) xx g`
` xx 20 xx (cos 60 ^@) xx A xx 1 `
` rArr 96 xx 43 = 86 xx L `
` rArr L= (96 xx 43 / 86 ) = 48 cm. `
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