Gallium melts just above room temperature and is liquid over a very wide temperature range (30-2204 °C), which means it would be a suitable fluid for a high-temperature barometer. Given its density, daa = 6.0 g/cm, what would be the height of the column if gallium is used as the barometer fluid and the external pressure is 9.5 x 10^4 Pa?

I need help finding the answer.

Well, well, well, looks like we have a gallium barometer puzzle on our hands! Don't worry, I'm here to clown around and help you out.

To calculate the height of the gallium column, we can use the equation:

Pressure = Density × Gravitational Acceleration × Height

Given that the pressure is 9.5 × 10^4 Pa and the density of gallium (daa) is 6.0 g/cm^3, we need to convert the density to SI units:

Density = 6.0 g/cm^3 = 6000 kg/m^3

Next, we can rearrange the equation to solve for the height:

Height = Pressure / (Density × Gravitational Acceleration)

Plugging in the values:

Height = (9.5 × 10^4 Pa) / (6000 kg/m^3 × 9.8 m/s^2)

Now, let's do the math:

Height = (9.5 × 10^4) / (6000 × 9.8)

Height ≈ 1.63 meters

So, if gallium is used as the barometer fluid and the external pressure is 9.5 × 10^4 Pa, the height of the gallium column would be approximately 1.63 meters.

I hope that brought a little laughter to your barometer conundrum!

To find the height of the column of gallium in the barometer, you can use the equation:

pressure = density x gravitational acceleration x height

First, convert the density of gallium from g/cm³ to kg/m³:
density (kg/m³) = density (g/cm³) x 1000

Given:
density (daa) = 6.0 g/cm³
external pressure = 9.5 x 10^4 Pa

density (kg/m³) = 6.0 g/cm³ x 1000 = 6000 kg/m³

Now rearrange the equation to solve for height:
height = pressure / (density x gravitational acceleration)

Substitute the given values:
height = (9.5 x 10^4 Pa) / (6000 kg/m³ x 9.8 m/s²)

Simplify:
height = 9.5 x 10^4 Pa / 58800 kg·m·s⁻²

Calculate the height:
height = 1.615 m

Therefore, the height of the column of gallium in the barometer would be approximately 1.615 meters.

To find the height of the column of gallium in the barometer, you can use the concept of hydrostatic pressure.

The hydrostatic pressure (P) at a certain depth (h) in a fluid is given by the equation:

P = ρ * g * h

Where:
- P is the pressure at depth h
- ρ is the density of the fluid
- g is the acceleration due to gravity (approximately 9.8 m/s²)
- h is the height of the column in meters

In this case, the density of gallium (ρ) is given as 6.0 g/cm³. To use this value in the equation, you need to convert it to kilograms per cubic meter (kg/m³). Since 1 g/cm³ = 1000 kg/m³, the density becomes 6000 kg/m³.

Now, you need to rearrange the equation to solve for h:

h = P / (ρ * g)

Given that the external pressure (P) is 9.5 x 10^4 Pa, the density (ρ) is 6000 kg/m³, and the acceleration due to gravity (g) is 9.8 m/s², substitute these values into the equation to find the height (h) of the column:

h = (9.5 x 10^4 Pa) / (6000 kg/m³ * 9.8 m/s²)

By multiplying and dividing the units correctly, you will get the height in meters.

consider the weight of a column of Gallium of area 1m^2

weight=9.8N/kg*1m^2*h*density

but weight=pressure*1m^2
change 6g/cm^3 to kg/m^3
6g/cm^3*1e6cm^3/m^3 * 1kg/1e3g)
= 6e3 kg/m^3 then
9.5e4=9.8*h*6e3
height= 95/(9.8*6)=1.62 meters

mental check: height of water column at 101kPa is 10 m, this is about 6x as dense as water, so h=about 10/6=1.7m