Question

The figure exemplifies a very long glass tube sealed at one end, which has been filled with a liquid (illustrated in green for better contrast). Then, this tube is placed with its open end against a container holding the same liquid. As a result, a vacuum region is produced in the upper part of the tube, which has the sealed end. Determine the height that the liquid column would reach inside the tube in the case of the following liquids: (a) Mercury ( ( 13534 mathrm{~kg} / mathrm{m}^{3} ) ). (b) Water ( left(1000 mathrm{~kg} / mathrm{m}^{3} ight) ). (c) Galinstan* ( left(6440 mathrm{~kg} / mathrm{m}^{3} ight) ). Additionally, (d) how would your answers change if the vacuum were replaced by air at ( 0.05 mathrm{~atm} ) ? Hint: compare the pressure at points ( mathrm{A} ) and ( mathrm{B} ) indicated in the figure. Please show the steps and calculations clearly and thoroughly. *Galinstan is a metallic alloy of gallium, indium, and tin that is liquid at room temperature. Answers: (a) ( 0.764 mathrm{~m} ) (b) ( 10.3 mathrm{~m} ) (c) ( 1.61 mathrm{~m} ) (d) ( 0.726 mathrm{~m}, 9.82 mathrm{~m} ), and ( 1.53 mathrm{~m} ), respectively.

          The figure exemplifies a very long glass tube sealed at one end, which has been filled with a liquid (illustrated in green for better contrast). Then, this tube is placed with its open end against a container holding the same liquid. As a result, a vacuum region is produced in the upper part of the tube, which has the sealed end.

Determine the height that the liquid column would reach inside the tube in the case of the following liquids:
(a) Mercury ( ( 13534 mathrm{~kg} / mathrm{m}^{3} ) ).
(b) Water ( left(1000 mathrm{~kg} / mathrm{m}^{3}
ight) ).
(c) Galinstan* ( left(6440 mathrm{~kg} / mathrm{m}^{3}
ight) ).

Additionally, (d) how would your answers change if the vacuum were replaced by air at ( 0.05 mathrm{~atm} ) ? Hint: compare the pressure at points ( mathrm{A} ) and ( mathrm{B} ) indicated in the figure.

Please show the steps and calculations clearly and thoroughly.
*Galinstan is a metallic alloy of gallium, indium, and tin that is liquid at room temperature.

Answers:
(a) ( 0.764 mathrm{~m} )
(b) ( 10.3 mathrm{~m} )
(c) ( 1.61 mathrm{~m} )
(d) ( 0.726 mathrm{~m}, 9.82 mathrm{~m} ), and ( 1.53 mathrm{~m} ), respectively.

The figure exemplifies a very long glass tube sealed at one end, which has been filled with a liquid (illustrated in green for better contrast). Then, this tube is placed with its open end against a container holding the same liquid. As a result, a vacuum region is produced in the upper part of the tube, which has the sealed end.

Determine the height that the liquid column would reach inside the tube in the case of the following liquids:
(a) Mercury ( ( 13534 mathrm kg / mathrmm^3 ) ).
(b) Water ( left(1000 mathrm kg / mathrmm^3
ight) ).
(c) Galinstan* ( left(6440 mathrm kg / mathrmm^3
ight) ).

Additionally, (d) how would your answers change if the vacuum were replaced by air at ( 0.05 mathrm atm ) ? Hint: compare the pressure at points ( mathrmA ) and ( mathrmB ) indicated in the figure.

Please show the steps and calculations clearly and thoroughly.
*Galinstan is a metallic alloy of gallium, indium, and tin that is liquid at room temperature.

Answers:
(a) ( 0.764 mathrm m )
(b) ( 10.3 mathrm m )
(c) ( 1.61 mathrm m )
(d) ( 0.726 mathrm m, 9.82 mathrm m ), and ( 1.53 mathrm m ), respectively.

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