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Pressure vs Velocity

A 10 cm colum...

Question

A 10 cm column of air is trapped by a column of mercury, 8 cm long, in a capillary tube horizontally fixed as shown below, at 1 atm pressure. When the tube is held at certain $θ^{o}$ , with open end up, the weight of Hg is borne partially by the gas. Vertical Height of Hg is a measure of additional pressure on gas
The length of air column, when the tube is fixed vertically at the same temperature with open end up is?

\frac{76 \times 84}{10}

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\frac{76 \times 10}{84}

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\frac{84 \times 10}{76}

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\frac{76 \times 10}{68}

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Solution

The correct option is D $\frac{76 \times 10}{68}$ cm
According to Boyle's law, at constant temperature,
$\begin{matrix} P V = constant {P = Pressure, V = V olume} ∴ P_{1} V_{1} = P_{2} V_{2} P_{1} l_{1} a = P_{2} l_{2} a \Rightarrow P_{1} l_{1} = P_{2} l_{2} \end{matrix}$
$\begin{matrix} l_{2} & = \frac{P_{1} l_{1}}{P_{2}} P_{1} & = 76 c m H g l_{1} = 10 c m P_{2} = & P_{1} - 8 c m of H g = & 76 - 8 = & 68 c m H g Now, l_{2} = & \frac{76 \times 10 c m}{68} c m \end{matrix}$
Hence (D) option is correct

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Similar questions

Q. A

10 c m

column of air is trapped by a column of

H g, 8 c m

long, in a capillary tube horizontally fixed as shown below, at

1 a t m

pressure. Calculate the length of air column where the tube is fixed at the same temperature (a) vertically with open end up (b) vertically with open end down. (c) at

45^{\circ}

with the horizontal with open end up.

Q. A

10.0 cm

column of air is trapped by a column of 4 cm long

H g

in a capillary tube of uniform bore when the tube is held horizontally at

1 atm

. The length of the air column when the tube is held vertically with the open end up is:
Given:

P_{a t m} = 76

cm of Hg

Q. A 10-cm column of air is trapped by an 8-cm-long column of Hg in a capillary tube horizontally fixed as shown in the figure at 1 atm pressure.
(a) vertically with open end up
(b) vertically with open end down
(c) at

45^{0}

from horizontal with the open end up

Q. A

10.0 cm

column of air is trapped by a column of 4 cm long

H g

in a capillary tube of uniform bore when the tube is held horizontally at

1 atm

. The length of the air column when the tube is held vertically with the open end up is:
Given:

P_{a t m} = 76

cm of Hg

A 10 cm long gas column is trapped by a 4 cm long column of mercury in a capillary tube, as shown below, when the tube is held horizontally in a room at an external pressure of 1 atm. The length of the air column when the tube is held vertically with the open end up is

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The correct option is D 76×1068cmAccording to Boyle's law, at constant temperature,PV= constant {P= Pressure ,V=Volume }∴P1V1=P2V2P1l1a=P2l2a⇒P1l1=P2l2l2=P1l1P2P1=76cmHg l1=10 cmP2=P1−8 cm of Hg=76−8=68 cmHg Now, l2=76×10 cm68 cmHence (D) option is correct