Respuesta :
The ideal gas equation and the pressure in barometer allows us to find the amount of air that we must introduce into the barometer for the change in height of the mercury column is:
- The variation of the volume is: ΔV = 7.67 cm³
Pressure is defined by the relationship between force and area.
P = F / A
The ideal gas equation establishes a relationship between pressure, volume, and temperature of an ideal gas.
PV = nR T
Where P is pressure, V is volume, and T is temperature.
Let's write this equation for two points assuming that the temperature has not changed.
P₀ V₀ = P₁ V₁
V₁ = [tex]\frac{P_o}{P_1} \ V_o[/tex] (1)
The subscript "o" is used for the start point and the subscript "1" for the end point.
The pressure in a barometer is:
P = ρ g y
They indicate the initial height of the barometer y₀=75 cm, the distance from empty space y'₀ = 9 cm and the final height of the barometer y₁ = 59 cm.
The volume of the cylinder is
V = π r² y
Let's calculate the initial volume.
V₀ = π 1 9
V₀ = 28.27 cm³
We substitute in equation 1.
V₁ = [tex]\frac{\rho \ g \ y_o}{\rho \ g \ y_1} \ V_o[/tex]
V₁ = [tex]\frac{y_o}{y_1} \ V_o[/tex]
Let's calculate.
V₁ = [tex]\frac{75}{59} \ 27.27[/tex]
V₁ = 35.94 cm³
The volume to be incremented is
ΔV = V₁ - V₀
ΔV = 35.94 - 28.27
ΔV = 7.67 cm³
Using the ideal gas equation and the pressure in barometer we can find the amount of air that we must introduce into the barometer for the change in height of the mercury column is:
- The change of the volume is: ΔV = 7.67 cm³
Learn more here: brainly.com/question/17254541
